What is the solution of the equation 7^(3x-2)=17 in terms of logarithms?

7^(3x-2) = 17

First we will
apply the logarithm for both sides.

==> log 7^(3x-2)
= log 17.

Now we will use the logarithm properties to solve
for x.

We know that log a^b = b*log
a.

==> log 7^(3x-2) = (3x-2)*log
7.

Let us substitute into the
equation.

==> (3x-2)*log 7 = log
17.

Now we will divide by log
7.

==> (3x-2) = log 17 / log
7.

Now we will add 2 to both
sides.

==> 3x = (log 17/log 7)  +
2

Now we will divide by
3.

==> x = [(log 17/log 7) + 2 ] /
3