logarithms help please

Question

Express in terms of sums and differences of logarithms: log?((10 x^2 y^5)/√z ) Show work.

Answer 1

The identities for logs of products and ratios are:

 

(1)   log(a*b) = log(a) + log(b),

 

(2)   log(a/b) = log(a) - log(b).

 

(1) can be extended to an expression for the log of a number raised to a power...

 

(3)   log(a*a*a*...*a) = log(a) + log(a) + log(a) + ... +log(a) = n*log(a), where n is the number of "a"s in the product.  Or stated differently,

 

(3) log(a^n) = n*log(a)

 

Using these relationships repeatedly yields

 

log((10 x^2 y^5)/√z ) = log(10) + 2*log(x) + 5*log(y) - (1/2)*log(z)

 

 

Answer 2

log?((10 x^2 y^5)/√z )I have no idea what the question mark means. I will expand

log((10 x^2 y^5)/√z )=log10+2logx+5logy-(1/2)logz