If x is a real number such that log3 5 = log5 (2 + x)

Question

Hello sir, please help me with this question.

Answer 1

log3(5) = log5(2+x)

5^log3(5) = 2 + x

5^log3(5) - 2 = x

log base 3 of (5) is just a number. The calculator says it is equal to 1.465 rounded to three decimal places.

5^1.465 - 2 = x $\approxeq$ 8.568 (rounded to 3 decimal places)