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Answer 1 · 2016-04-04T19:40:41

#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 #2ln(3)# it is another way of writing #ln(3^2)#

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given: #ln(t)=ln(5)+2ln(3)#

Write as #ln(t)=ln(5)+ln(3^2)#

Write as #ln(t)=ln(3^2xx5)#

#=>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

#=>t=45#