Having trouble getting started on a few of these.
1. 5^(x-10) = 125^x
2. (3/4) log x ^(3/4) + 9 = 0
thanks again!
Hello, Hapa!
We have: .$\displaystyle 5^{x-10} \;=\;\left(5^3\right)^x \quad\Rightarrow\quad 5^{x-10} \:=\:5^{3x}$$\displaystyle 1)\;\;5^{x-10} \:=\: 125^x$
Equate exponents: .$\displaystyle x-10 \:=\:3x\quad\hdots\;\text{ etc.}$
$\displaystyle 2)\;\;\tfrac{3}{4}\log\left(x ^{\frac{3}{4}}\right) + 9 \:=\: 0$
We have: .$\displaystyle \tfrac{3}{4}\log\left(x^{\frac{3}{4}}\right) \:=\:-9 \quad\Rightarrow\quad \tfrac{3}{4}\cdot\tfrac{3}{4}\log(x) \:=\:-9 \quad\Rightarrow\quad \tfrac{9}{16}\log(x) \:=\:-9 $
. . . . . . $\displaystyle \log(x) \:=\:-16 \quad\Rightarrow\quad x \:=\:10^{-16} $
Edit: Too slow ... again!