Use the Laws of logarithms to rewrite the expression log5 3

Use the Laws of logarithms to rewrite the expression log_5 3 squareroot x^2 + 19 in a form with no logarithm of a product, quotient or power. After rewriting we have log_5 3 squareroot x^2 + 19 = A log_5 f(x) with the constant A = and the function f(x) =

Solution

Given logarithm can be written as

log₅ (x²+19)^1/3

= (1/3) log₅ (x²+19)

= A log₅ f(x)

Therefore,

A = 1/3

f(x) = (x²+19)