To solve for x in the equation 3^(2x) = 5, we can take the logarithm of both sides with base 3:
log3(3^(2x)) = log3(5)
Using the power rule of logarithms, we can simplify the left-hand side:
2x log3(3) = log3(5)
Since log3(3) = 1, we can further simplify:
2x = log3(5)
Dividing both sides by 2:
x = (1/2)log3(5)
Using the change of base formula, we can express this in terms of a common logarithm or a natural logarithm:
x = (1/2)log3(5) = (1/2)(log10(5)/log10(3)) ≈ 0.6832
or
x = (1/2)log3(5) = (1/2)ln(5)/ln(3) ≈ 0.6832
Therefore, the solution to the equation 3^(2x) = 5 is x ≈ 0.6832.