Solve a simple equation with log in it I'm stuck with

yert21trey123z7

yert21trey123z7

Answered question

2022-04-22

Solve a simple equation with log in it
I'm stuck with solving this equation,
2logx=log9
This is how far I made it:
logx=log4,5
x=?I'm a beginner at logarithms so I appreciate ways to solve it and not just an answer.

Answer & Explanation

Adrien Ho

Adrien Ho

Beginner2022-04-23Added 16 answers

If we start with
2logx=log9,
the first step is to move the 2, but you can't divide it over like that. The rule is that alogb=logba , so we get 2logx=PSKlogx2.
Now our equations is
logx2=log9.
The next step is to use the fact that logA=logB means A=B.In our case, that means
x2=9,
and you can solve for x. Remember to check that the answer makes sense. For instance 9=±3 but you can't take the log of a negative, so x3
kweefomucy9

kweefomucy9

Beginner2022-04-24Added 13 answers

Note that 12log9log92. Instead 12log9=log912=log3 constants become powers when you take them inside the log.
Once you're in the situtation where you have the equation logx=logy, then taking exponentials of both sides gives you x=y.

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