Find the x-intercept of:
$3-4\log _{10}\left(2x\right) $
My process:
$4\log _{10}\left(2x\right)=3 $
$\log _{10}\left(2x\right)\:=\:\frac{3}{4}$
How would I find the x-intercept from here?
$\log _{10}\left(2x\right)\:=\: \log _{10}\left(?\right)\:$
$2x=?$
$xintercept=\frac{?}{2}$
How do I find the x-intercept?
$\endgroup$2 Answers
$\begingroup$you can write $$\log_{10}(2x)=\log_{10}10^{3/4}$$
$\endgroup$ $\begingroup$Let $$f(x)=3-4\log _{10}\left(2x\right) $$ and set$$f(x)=0$$ which gives
$$3=4\log _{10}(2x)$$ $$\frac34=\log _{10}(2x)$$ Now $\log_ab=c$ implies $a^c=b$ or like you have done $\log_{10}(2x)=\log_{10}10^{3/4}$ which gives $$10^{3/4}=2x$$ $$x=\frac{10^{3/4}}{2}$$
$\endgroup$ 2
