Question

Solve for x when.. log(base10)x+log(base10)(x-3)=1

Answer 1

\[\log_{10}x+\log_{10}(x-3)=1 \]

Answer 2

First, write the two logs on the left as a single log using the product rule for logs

Answer 3

so \[\log_{10} x(x-3)=1\] ??

Answer 4

Yah!!! good. So now rewrite the log equation as an exponential equation.

Hint: \(\large \log_b(x) = y\) if and only if \(\large b^y = x\)

Answer 5

\[x ^{2}-3x-1=0\]x

Answer 6

almost. that 1 should be 10,

\[\large x(x-3) = 10^1\]

Answer 7

ooooooooo okay see I was going to do that but wasn't sure if that seemed right. So then from there factor it out and solve for x?

Answer 8

You got it!

Answer 9

Ooh wow it's actually not that hard Thank you so much!