Question

If log (a) x = 7, what is the value of log a (a/ x^2) ?
Thank you!

Answer 1

It can be simplified to log(a) a - 2 log (a)x= 1-14= -13

Answer 2

well apply the log law for division and you get

\[\log_{a}(\frac{a^1}{x^2}) = \log_{a} (a^1)- \log_{a}(x^2)\]

and you should know

\[\log_{a}(a) = 1\]

or is equal to the power

so its

\[1 - \log_{a}(x^2)\]

now apply the log law for indexes to the 2nd term

\[\log(m^b) = b \times \log(m)\]

then you should have an expression in terms of log(x)

hope it helps

Answer 3

Thank you!
What do m and b represent?

Answer 4

in you're question its

x^2

Answer 5

So m represents x and b represents root 2?

Answer 6

I'm still not quite sure how to solve this.

Answer 7

well if you look at it the simplification using log laws becomes

\[\log_{a}(a^1) - \log_{a}(x^2) = 1 - 2 \times \log_{a}(x)\]

and you know the value of log(x)

so substitute it and then find the value.

Answer 8

I just tried to solve it and got 1.535, but I don't think thats right.

Answer 9

ok... so you know

\[\log_{a}(x) = 7\]

that piece of information is given in the question so then

\[1 - 2 \times \log_{a}(x) = 1 - 2 \times 7 \]

Answer 10

Oh! So it's -13?

Answer 11

thats it