Condense to a single logarithm: log 3𝑥 + log(2𝑥 − 1) − 4 log 5𝑥

Question

Please help me a step by step

Answer 1

Logarithms follow multiplication rule for addition means if two separate log of same base adds up then we multiply value and if they are in subtraction then they are in division.

log3x+log(2x-1)-4log5x

=log(3x)(2x-1)-log(5x)⁴

=log(3x)(2x-1)/(5x)⁴

=log{3(2x-1)}/(625x³)

Answer 2

Use log rules log(a)+log(b) = log(ab), log(a)-log(b) = log(a/b) and alog(b) = log(b^a)

log(3x)+log(2x-1)-4log(5x)

log(3x(2x-1)/(5x)⁴)

simplifying:

log(3(2x-1)/(5⁴x³))