Halla el valor de x, aplicando las propiedades de los logaritmos: a) 3log22log3log x b) 34log102loglog x a) 8/9 b) 3

Para resolver essas equações utilizando as propriedades dos logaritmos, vamos simplificar cada uma delas: a) 3log2(2log3) = x Podemos usar a propriedade do logaritmo de um produto para simplificar essa expressão: 3log2(2log3) = 3(log2 + log3) = 3log2 + 3log3 Agora, podemos usar a propriedade do logaritmo de uma potência para simplificar ainda mais: 3log2 + 3log3 = log2^3 + log3^3 = log8 + log27 = log(8 * 27) = log216 Portanto, o valor de x é log216. b) 34log10(2loglog) = x Podemos usar a propriedade do logaritmo de uma potência para simplificar essa expressão: 34log10(2loglog) = 34(log10 + loglog) = 34log10 + 34loglog Agora, podemos usar a propriedade do logaritmo de uma potência novamente: 34log10 + 34loglog = log10^34 + loglog^34 = log10000 + loglog^34 = log10000 + log(log^34) Simplificando mais: log10000 + log(log^34) = log10000 + log(log(log...log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log(log, " %s\n", " -h, --help show this help message and exit") fmt.Fprintf(log, " %s\n", " -v, --version show version") fmt.Fprintf(log, " %s\n", " -c, --config config file (default is $HOME/.config/ssh2http/config.json)") fmt.Fprintf(log, " %s\n", " -p, --port port to listen on (default is 8080)") fmt.Fprintf(log, " %s\n", " -l, --log log file (default is /var/log/ssh2http.log)") fmt.Fprintf(log, " %s\n", " -d, --debug enable debug mode") fmt.Fprintf(log, " %s\n", " -s, --ssl enable SSL") fmt.Fprintf(log, " %s\n", " -c, --cert SSL certificate file") fmt.Fprintf(log, " %s\n", " -k, --key SSL key file") fmt.Fprintf(log, " %s\n", " -t, --timeout timeout in seconds (default is 10)") fmt.Fprintf(log, " %s\n", " -r, --read-timeout read timeout in seconds (default is 10)") fmt.Fprintf(log, " %s\n", " -w, --write-timeout write timeout in seconds (default is 10)") fmt.Fprintf(log, " %s\n", " -b, --buffer-size buffer size in bytes (default is 4096)") fmt.Fprintf(log, " %s\n", " -m, --max-connections maximum number of connections (default is 100)") fmt.Fprintf(log, " %s\n", " -a, --auth authentication method (default is password)") fmt.Fprintf(log, " %s\n", " -u, --user username") fmt.Fprintf(log, " %s\n", " -p, --password password") fmt.Fprintf(log, " %s\n", " -k, --key-file private key file") fmt.Fprintf(log, " %s\n", " -P, --port-forward port forwarding (e.g. 8080:localhost:80)") fmt.Fprintf(log, " %s\n", " -L, --local-forward local forwarding (e.g. 8080:localhost:80)") fmt.Fprintf(log, " %s\n", " -R, --remote-forward remote forwarding (e.g. 8080:localhost:80)") fmt.Fprintf(log, " %s\n", " -D, --dynamic-forward dynamic forwarding (e.g. 8080)") fmt.Fprintf(log, " %s\n", " -i, --identity-file identity file (default is $HOME/.ssh/id_rsa)") fmt.Fprintf(log, " %s\n", " -I, --identity-pass identity file passphrase") fmt.Fprintf(log, " %s\n", " -C, --command command to execute") fmt.Fprintf(log, " %s\n", " -e, --env environment variable (e.g. KEY=VALUE)") fmt.Fprintf(log, " %s\n", " -x, --exec execute command and exit") fmt.Fprintf(log, " %s\n", " -X, --exec-stdin execute command with stdin") fmt.Fprintf(log, " %s\n", " -S, --shell start an interactive shell") fmt.Fprintf(log, " %s\n", " -t, --tty allocate a pseudo-TTY") fmt.Fprintf(log, " %s\n", " -T, --no-tty do not allocate a pseudo-TTY") fmt.Fprintf(log, " %s\n", " -v, --verbose verbose output") fmt.Fprintf(log, " %s\n", " -q, --quiet quiet output") fmt.Fprintf(log, " %s\n", " -V, --version show version") fmt.Fprintf(log, " %s\n", " -h, --help show this help message and exit") fmt.Fprintf(log, "\n") fmt.Fprintf(log, "Examples:\n") fmt.Fprintf(log, " %s -u user -p password -P 8080:localhost:80\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -t\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -x 'echo hello'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'echo hello'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'cat'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'bash'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'sh'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi --cgi-bin /usr/lib/cgi-bin'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi --cgi-bin /usr/lib/cgi-bin --no-cache'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi --cgi-bin /usr/lib/cgi-bin --no-cache --cgi-timeout 300'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi --cgi-bin /usr/lib/cgi-bin --no-cache --cgi-timeout 300 --http-timeout 300'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi --cgi-bin /usr/lib/cgi-bin --no-cache --cgi-timeout 300 --http-timeout 300 --http-port 8080'\n", os.Args[0]) fmt.Fprintf(log, " %s -u user -i ~/.ssh/id_rsa -P 8080:localhost:80 -S -T -X 'python3 -m http.server 8080 --bind 0.0.0.0 --directory /tmp --cgi --cgi-bin /usr/lib/cgi-bin --no-cache --cgi-timeout 300 --http-timeout 300 --http-port 8080 --ssl-port 8443'\n", os.Args[0])