What is the solution for 3.5^(3x + 1) = 65.4?

We have to find the solution for the equation 3.5^(3x + 1)
= 65.4

An easy way to determine the value for x is to use
logarithms. Take the log of both the sides

log 3.5^(3x + 1)
= log 65.4

use the the property of logarithms that log a^b
= b*log a

=> (3x + 1)* log 3.5 = log
65.4

=> 3x + 1 = log 65.4 / log
3.5

=> 3x = (log 65.4 / log 3.5) -
1

=> x = [(log 65.4 / log 3.5)]/3 -
1/3

=> x = 0.7790
approximately

The required value of x = [(log
65.4 / log 3.5)]/3 - 1/3