Question

Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x, and log y.

log x^3 y^4

Answer 1

log x³ y⁴ = 3 log ( x ) + 4 log( y)

Explanation:

Given function log x³ y⁴

step(i):-

Applying logarithmic formula

log ( a b ) = log (a) +log (b)

log x³ y⁴ = log ( x³ ) + log( y⁴)

step(ii):-

Applying logarithmic formula

log (x ⁿ) = n log x

log x³ y⁴ = log ( x³ ) + log( y⁴)

log x³ y⁴ = 3 log ( x ) + 4 log( y)

final answer:-

log x³ y⁴ = 3 log ( x ) + 4 log( y)