Question

i'll type my question in the comments:D

Answer 1

\[1-\log_{\sqrt{10}} (x+5)+\log(x+10)=0\]

Answer 2

so faaaaar i made 1=log10 then
i made the 2nd term 2log(x+5)? since log(x+5)/logsqrt10?

Answer 3

is it really log base root ten?

Answer 4

because if so, you can convert everything to log base ten and make it much easier

Answer 5

yup log base root ten if it's only indicated as "log" but the 2nd term is base √10 since it's indicated there :D

Answer 6

by the "change of base" formula
\[\log_{\sqrt{10}}(x)=\frac{\log_{10}(x)}{\log_{10}(\sqrt{10})}\]
\[=\frac{\log_{10}(x)}{\frac{1}{2}}=2\log_{10}(x)\]

Answer 7

yup that's what i did! :D up there in my comment :D sooo was that right?

Answer 8

meaning you can start with
\[1-2\log (x+5)+\log(x+10)=0\]

Answer 9

oh yes, you are right. proceed from there

Answer 10

it is not a bunch of algebra, only one more trig step
\[1-\log((x+5)^2)+\log(x+10)=0\]
\[\log\left(\frac{(x+5)^2}{(x+10)}\right)=1\] etc

Answer 11

*now a bunch of algebra

Answer 12

OHHHHHH I'M GETTING IT THANK YOUUU!! i got stuck there!