Question

If log10(x-2) - 3log10(2x)=1-log10(y) then y is equal to? Working out please :D
The answer is (80x^3)/x-2

Answer 1

do u know the rules of logarithms?

Answer 2

when u have log a - log b = log (a/b)
and alogb = logb^a

so here
log10 (x-2) - log10 (2x)^3 = 1-log10 y
it becomes
log10 (x-2)/(2x)^3 = 1-log10 y

Answer 3

and we also know that
log a + log b = log a*b

so
log10 (x-2)/(2x)^3 +log10 y =1

so log10 ((x-2)/8x^3)y =1
10^1 =( x-2 / 8x^3)y
y= 80x^3 / x-2

Answer 4

Thanks for your help. Yeah i need to brush up on my log rules xD

Answer 5

yur welcome :D