Chapter 11.6, Problem 3CFU

To determine

The verification of $\ln 64=\ln 16+\ln 4=2\ln 8$

Explanation of Solution

Now we know that, according to the logarithmic product rule,

  $\ln (a\times b)=\ln a+\ln b$

Therefore we can write,

  $\ln 64=\ln (16\times 4)$

Thus, according to the logarithmic product rule,

  $\ln 64=\ln (16\times 4)=\ln 16+\ln 4$

Also, according to the logarithmic power rule,

  $\ln a^b=b\ln a$

Therefore, according to the logarithmic power rule,

  $\ln 64=\ln 8^2=2\ln 8$

Thus we can write,

  $\ln 64=\ln 16+\ln 4=2\ln 8$

Thus it is verified.