# College Algebra

I am asked to write a logarithmic expresion as a single logarithm with coefficient 1 and simplify as much as possible. The equation is:

4logbase5Y-3logbase5X+1/2logbase5Z.

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1. first of all, it's just an expression, not an equation (no = sign)

Since loga + logb = log(a*b)
just a x^a * a^b = x^(a+b)

log x^n = log(x*x*x*x...)= n*logx

assuming logs base 5, but the base does not matter if all the logs are to the same base; the rules apply regardless of the base

4logx-3logy + 1/2 logz
= log(x^4√z/y^3)

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posted by Steve

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