Logarithm question: Is my answer correct or not?

Hi,

I have a question: Solve for X in the equation 3log5(1/4) - log5X = 3

I keep getting X=0.000125 when the answer is 8000.

Thanks

Student X

You are correct, answer provided is wrong.

3log5(1/4) - log5X = 3

3 [ log5(1) - log5(4) ] - log5X =3

3 [ 0 - log5(4) ] - log5X=3

log5X = -3 log5(4) -3 = log5(1/64) - 3

        = log5(1/64) + log5(1/125)

        = log5(1/8000)

Hence, by direct comparison of content of logarithms on both sides, we arrive at X =1/8000 (shown)

PS: Anyways I did a substitution of X=1/8000 ( = 0.000125) back into the original equation and things do balance up, so your answer is a thousand percent right.

Hope this helps. Peace.

Best Regards,

Mr Koh