Question

HELP
Solve 2logx+log4=2 without a calculator.
i know its so simple, but i haven't done these in a while please help.

Answer 1

Remember your log rules: \[\log(a)+ \log(b) = \log(ab)\]\[\log(x^2) = 2\log(x)\]

Answer 2

which one would i use for my problem ? the first one correct ?

Answer 3

Both.

Answer 4

4 is a perfect square, meaning \(4 = 2^2\). That's a hint.

Answer 5

so x would be? i don't get it /

Answer 6

\(\color{blue}{\text{Originally Posted by}}\) @Jhannybean
Remember your log rules: \[\log(a)+ \log(b) = \log(ab)\]\[\log(x^2) = 2\log(x)\]
\(\color{blue}{\text{End of Quote}}\)

using the first rule, let's let \(a=x\) and \(b= 4\)
Now lets rewrite it to fit the log rule: \(\log(a^2) +\log(b) =2\)

Can you rewrite the left hand side of the equation for me following the log rules ?

Answer 7

log(x^2) + log(4)=2

Answer 8

And so when youre adding two log functions together, the functions multiply, giving you \[\log(4x^2)=2\]

Answer 9

Understanding that so far

Answer 10

okay so the answer would be x=5 correct?

Answer 11

I believe so. \[\log((2x)^2)= 2\]\[2\log(2x) = 2\]\[\log(2x) = 1\]\[10^{\log(2x)} =10^1\]\[2x=10\]\[x=5~~ \checkmark\]

Answer 12

okay thank you ! ima post another question right now :)