# Question #833f2

Apr 4, 2016

$t = 45$

#### Explanation:

There are several thing to remember about logs.

Logs being added means the source numbers are multiplied

Not in your question: Loges being subtracted means that the source numbers are divided

Logs being multiplied mean that for $2 \ln \left(3\right)$ it is another way of writing $\ln \left({3}^{2}\right)$

Not in your question: For loges being divided, say $\ln \frac{x}{2}$ it is another way of writing $\ln \left(\sqrt{x}\right)$

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Given: $\ln \left(t\right) = \ln \left(5\right) + 2 \ln \left(3\right)$

Write as $\ln \left(t\right) = \ln \left(5\right) + \ln \left({3}^{2}\right)$

Write as $\ln \left(t\right) = \ln \left({3}^{2} \times 5\right)$

$\implies \ln \left(t\right) = \ln \left(45\right)$

In my day they called it Anti Log. Now they call it Invers log.

Taking the invers log of both sides

$\implies t = 45$