Question

Use the properties of logarithms to expand the following expression.log(z3)/√x5y)Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive.

Answer 1

3 log (z) - 1/2log (x) - 1/2 log (5) -1/2 log y

Explanation:

log(z3)/√x5y)

= log (z3) - log (√x5y) [division being subtracted]

= 3 log (z) - {log (√x) + log (√5y)} [ multiplication being added in the denominator]

= 3 log (z) - {log (x)^1/2 + log (5)^1/2+ log (y)^1/2}

= 3 log (z) - 1/2{log (x) + log (5)+ log y }

We can solve inside the curly bracket and then multiply with 1/2 or we can solve it separately

= 3 log (z) - 1/2log (x) - 1/2 log (5) -1/2 log y

How does this work?

1) any two terms being multiplied in logarithms are added with the log of each.

2) the exponent becomes the co- efficient.

3) any two terms being divided in logarithms are subtracted with the log of each