Find the exact value of the logarithm without using a calcul

Find the exact value of the logarithm without using a calculator. log_1/5^652 log_1/5 625 = (Type an integer or a simplified fraction.)

since 625 = 5⁴ = (1/5)^-4

log_1/5(625) = log_1/5(1/5)^-4

since log(aⁿ)=nlog(a)

log_1/5(625) = -4 log_1/5(1/5)

since log_a(a)=1

log_1/5(625) = -4 (1)

log_1/5(625) = -4

$Find the exact value of the logarithm without using a calculator. log_1/5^652 log_1/5 625 = (Type an integer or a simplified fraction.)Solutionsince 625 = 54 =$

Find the exact value of the logarithm without using a calcul

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