Please Help! Simple Logarithm Equation?

Question

Let a = log x

Let b = log y

Let c = log z

Write log(base 10) [(x^2 (square root of y)) / z^3] in terms of a, b and c.

I got 4a + b - 6z as an answer, but I substituted numbers in for the variables and I got different answers, so I know that my answer isn't right.

Can someone please teach me how to do this equation?

I am choosing best answer! :)

Thanks!

Answer 1

Somehow you doubled everything.  Try

2a + 0.5 b -3 c.  

Answer 2

By rules of logarithm ,

we have

log ab/c = log a + log b - logc

log a^2 = 2loga [power rule]

  log (x² √y ) / z³

= log x² + log√ y - logz³

= 2logx +  log y^ 1/2 - 3 logz

= 2logx + (1/2) logy - 3 logz

= 2a + (1/2) b - 3c