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Answer 1 · 2016-04-04T19:40:41

$t = 45$ $t=45$

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 $2 ln (3)$ $2ln(3)$ it is another way of writing $ln (3^{2})$ $ln(3^2)$

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

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

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

Write as $ln (t) = ln (3^{2} \times 5)$ $ln(t)=ln(3^2xx5)$

$\Rightarrow ln (t) = ln (45)$ $=>ln(t)=ln(45)$

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

Taking the invers log of both sides

$\Rightarrow t = 45$ $=>t=45$