Question

if x= log (w) and y=log(z), what is log (wz^3) in terms of x and y.

Answer 1

Lets first represent x and y in terms of w and z

x = log (w).

If there is no base present we assume base is 10.

So, the formula for log is

log10y =x can be written as 10x = y

So, 10x = w

10y = z

Now,

log(wz^3)

substitute w and z with the values above,

log(10x x 10y)3

log(10x+y)3

log 103(x+y)

now for example if we have

log 102 we can write it as 2 log 10

similarly, here we can write it as

3(x+y) log 10

since log 10=1

the answer is 3(x+y) or 3x+3y.

if you have any doubts or require any clarifications, do let me know.

Thank you :)