Anyone can help me with this math question?

3ⁿ = 5ⁿ⁻¹
log(3ⁿ) = log(5ⁿ⁻¹)
n log(3) = (n - 1) log(5)
n log(3) = n log(5) - log(5)
n log(5) - n log(3) = log(5)
n [log(5) - log(3)] = log(5)
n = log(5) / [log(5) - log(3)]

n ≈ 3.15066

Given 3^n = 5^(n - 1),
the value of n:
n ≈ -1.9576 i (6.2832 m + 1.6094 i), m element Z

3ⁿ = 5ⁿ⁻¹
5 × 3^n = 5^n
Real solution:
n = log(5)/log(5/3)
n = -(i (2 π m + i log(5)))/(log(5) - log(3)), m element Z

Did you try symbolab?

ln(3^n) = ln(5^(n-1))
n ln3 = (n-1) ln5
n = ln5 / (ln5 - ln3)