How do you solve when you have logs on one side but not the other? (2 problems inside)

Question

anonymous · Answer

attachment

anonymous · Answer

use the product rule log A + log B = log (AB)

anonymous · Answer

I tried that... 
for Log x + log (x+15) = 2
I have (Log x)(log (x+15)) =2 
i dont know what to do after
The answer is 5

saifoo.khan · Answer

$$\lg x(x+15) = 2$$

raden · Answer

convert 2 to log 100

aravindg · Answer

log x+log (x+15)=log(x(x+15))!!

raden · Answer

it just a hint, so that both sides have log's :)

anonymous · Answer

But how do you go from 
log(x(x+15)=2.. to x=5? 
I can't get that part

raden · Answer

log(x(x+15))=2
log(x(x+15)=log100
cancel out the log, giving us :
x(x+15)=100 or
x^2+15x-100=0
solve for x by factorization or by complete square or by quadratic formula

raden · Answer

got it ?

anonymous · Answer

Yes! Just solved it.. thank you!

raden · Answer

yw

anonymous · Answer

I didn't think of doing log 100 to cancel the logs on both sides