# Thread: This is driving me crazy!!!! LOGS!!

1. ## This is driving me crazy!!!! LOGS!!

$\displaystyle 3^{4-3x}=4^{x+5}$

$\displaystyle 4log3 - 3xlog3 = xlog4 + 5log4$

$\displaystyle -3xlog3 - xlog4 = 5log4 - 4log3$

$\displaystyle x(-3log3 - log4) = 5log4 - 4log3$

$\displaystyle x = \frac{5log4 - 4log3}{(-3log3 - log4)}$

My answer is completely wrong, apparently it's -0.542 so i guess theres something up with my factorising?

2. ## You have it right

Your answer is indeed -0.542. Why do you think you have it wrong?

3. I was putting it into the calculator incorrectly.. oops!

4. Hello, Flexible!

$\displaystyle 3^{4-3x}\;=\;4^{x+5}$

$\displaystyle 4\log3 - 3x\log3 \;=\; x\log4 + 5\log4$

$\displaystyle -3x\log3 - x\log4 \;=\; 5\log4 - 4\log3$

$\displaystyle x(-3\log3 - \log4) \;=\; 5\log4 - 4\log3$

$\displaystyle x \;= \;\frac{5\log4 - 4\log3}{(-3\log3 - \log4)}$ . . . . All of this is correct!

Apparently it's -0.542

I bet you're entering it incorrectly into your calculator.

Suppose we want: .$\displaystyle \log2 + 3$

If we enter: .$\displaystyle \boxed{\text{log}}\;\;\boxed{2}\;\;\boxed{+}\;\;\b oxed{3}\;\;\boxed{=}$ ... we will get the wrong answer.

Press $\displaystyle \boxed{\text{log}}$ on your calculator.
. . On the display you will see: .log(
It automatically provides a left parenthesis in ancitipation of a longer quantity.
. . We are expected to provide the right parenthesis.

If we don't ... and we press: .$\displaystyle \boxed{\text{log}}\;\;\boxed{2}\;\; \boxed{+}\;\;\boxed{3}\;\;\boxed{=}$
. . the calculator reads it as: .log(2 + 3 =
. . and returns: .log 5

We must enter: .$\displaystyle \boxed{\text{log}}\;\;\boxed{2}\;\;{\color{blue}\b oxed{)}}\;\;\boxed{+}\;\;\boxed{3}\;\;\boxed{=}$

So an expression like: .$\displaystyle 5\log4 - 4\log3$ should be treated like this:

. . $\displaystyle \boxed{5}\;\;\boxed{\times}\;\;\boxed{\text{log}} \;\;\boxed{4} \;\;{\color{red}\boxed{)}}\;\;\boxed{-}\;\;\boxed{4}\;\;\boxed{\times}\;\;\boxed{\text{l og}}\;\;\boxed{3}\;\;{\color{red}\boxed{)}}$