Using an Exponent to Undo Log

What is the next step in solving this (using this method)? But there is another way which involves using the log laws (which I know how to do).

$\displaystyle \log x - \dfrac{1}{3}\log8 = \log7$

$\displaystyle 10^{\log(x)- \frac{1}{3}\log8} = 10^{\log7}$

I believe the next step involves dividing the bases of the exponents, since the exponents are subtracted.

Re: Using an Exponent to Undo Log

why r u doing this???

isnt log x=log7 +log2

use log a + log b= log ab

and find the answer

Re: Using an Exponent to Undo Log

An example of exponanted stuff:

$\displaystyle e^{\ln (2 + y^{2)}} = e^{\ln(4 + x^{2}) + C}$

$\displaystyle 2 + y^{2} = (4 + x^{2}) e^{C}$ Since adding, then multiplying comes in.

But with the other example on this page, some subtracting was in there.

Re: Using an Exponent to Undo Log

Do it with the laws of logarithms, you will get the answer straight unless you have a special purpose.

lox x - 1/3 log 8 = log 7

log x - log(8)^(1/3 ) = log 7

log x - log 2 = log 7

log ( x/2) = log 7 that will give x = 14

Re: Using an Exponent to Undo Log

Hello, Jason76!

Quote:

$\displaystyle \text{Solve for }x\!:\;\log x - \tfrac{1}{3}\log8 \:=\: \log7$

Simplify the logs *before* you exponentiate.

We have: .$\displaystyle \log x \:=\:\log 7 + \tfrac{1}{3}\log 8 $

. . . . . . . . $\displaystyle \log x \;=\;\log 7 + \log\left(8^{\frac{1}{3}}\right)$

. . . . . . . . $\displaystyle \log x \;=\;\log 7 + \log 2$

. . . . . . . . $\displaystyle \log x \;=\;\log(7\cdot2)$

. . . . . . . . $\displaystyle \log x \;=\;\log 14$

Therefore: n . $\displaystyle x \;=\;14$