Question

write log 72 in terms of log 2 and log 3



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Answer 1

Answer:

this is an answer It may help you

Answer 2

$\log 72$ can be written in terms of $\log 2$ and "$\log 3$ is $3\log 2 +2\log 3$".

Step-by-step explanation:

We have,

$\log 72$

To wtote, $\log 72$ in terms of $\log 2$ and $\log 3$ = ?

∴ 72 = 2 × 2 × 2 × 3 × 3

= $2^3\times 3^{2}$

∴  $\log 72$

= $\log (2^3\times 3^{2})$

Using the logarithm identity,

$\log ab= \log a+\log b$

= $\log 2^3 +\log 3^{2}$

Using the logarithm identity,

$\log a^m=m\log a$

= $3\log 2 +2\log 3$

∴ $\log 72$ can be written in terms of $\log 2$ and $\log 3$ = $3\log 2 +2\log 3$

Thus, $\log 72$ can be written in terms of $\log 2$ and "$\log 3$ is $3\log 2 +2\log 3$".