Question

HELP ASAP. MEDAL GIVEN
Solve the equation below for x:
log(5x) + log(2x) =1

x = 10/7
x = 1
x = 1; x = -1
There is no solution.

Answer 1

At first lets use the identity,
\[\color{blue}{Log(a)+Log(b)=Log(a \times b) }\]
so the left side equals \[\log(5x \times 2x)\]so, so far we have\[\log(10x^2)=1\]

can you solve it from here?

Answer 2

Honestly No... -_-

Answer 3

\[\color{red}{ \log(10x^2)=1 }\]\[\color{red}{ 2\log(10x)=1 }\]\[\color{red}{ \log(10x)=1/2 }\]what about now?

Answer 4

Umm, I honestly don't know what any of that is suppose to mean.. im not that bright in math

Answer 5

Oh nvm I mad a mistake

Answer 6

\[\color{orangered}{\log(10)+\log(x^2)=1 }\]
when base is not specified, it's equal to 10.
\[\color{orangered}{\log_{10}(10)+\log_{10}(x^2)=1 }\]\[\color{orangered}{1+\log_{10}(x^2)=1 }\]\[\color{orangered}{\log_{10}(x^2)=0 }\]

you should be able to do it from here.

Answer 7

1 ?

Answer 8

\[\log_{10}(x^2)=0\]\[2\log_{10}(x)=0\]\[\log_{10}(x)=0\]\[x=1\]

Answer 9

you are right!

Answer 10

thanks :)

Answer 11

You Welcome!