Question

Fill in the blank so that the resulting statement is true.

Answer 1

5x-2=13

Step-by-step explanation:

Take the log of both sides

log
`3^(5x-2)` = log
`3^(13)`

Move the exponents down

(5x-2) log 3 = 13 log 3

Divide both sides by log 3

(5x-2) log 3/log 3 = 13 log 3/log 3

log 3 cancels out on both sides

5x-2=13

Answer 2

`\boxed{\sf 5x-2} = 13`

Step-by-step explanation:

`\sf \rightarrow 3^(5x-2)=3^(13)`

`\sf \rightarrow 5x-2=13`

`\sf \rightarrow 5x=13+2`

`\sf \rightarrow 5x=15`

`\sf \rightarrow x=3`

Additional comment: If the bases are same on the both sides then cancel them out. For example:
`a^b = a^c` then
`b = c`.