Solving for $x$ in $10.000\times 1,0877^{x-20} = 8.028.000$ I'm not good with math, so you could really help me out.
I have this formula:

$$10.000\times 1,0877^{x-20} = 8.028.000$$ 

What is $x$? Can I do the following?  

$$10.877^{x-20} = 8.028.000$$

And then what?
Thanks in advance :)
 A: No you can't since
$$A\cdot B^{(x-20)}\neq (A\cdot B)^{(x-20)}$$
we need to proceed as follows
$$A\cdot B^{(x-20)}=C \implies B^{(x-20)}=\frac C A \implies \log_B\left(B^{(x-20)}\right)=\log_B\left(\frac C A\right)$$
$$\implies x-20=\log_B\left(\frac C A\right) \implies x=20+\log_B\left(\frac C A\right)\implies x=20+\frac{\log \left(\frac C A\right)}{\log B}$$
where we have used that $\log x^y=y\log x$ and $\log_x y= \frac{\log y}{\log x}$.
A: Assuming by $8.028.000$ you mean $8028000$?
$x \approx 20.72 $
Since:
$10000\times(10877)^{(x-20)} = 8028000 $ implies $10877^{(x-20)} = {8028\over10}$
and so $ x-20 = {{\ln({8020\over10})}\over{\ln(10877)}} \approx 0.72$
Apologies if I have interpreted the question wrongly. If you just need the answer to this kind of thing https://www.wolframalpha.com/ can solve it for you.
A: $$10000\cdot1,0877^{x-20}=8028000$$
To solve for $x$, first divide left and right side by $10000$:
$$1,0877^{x-20} = 802,8$$
If right-side = left side then use natural log: $\ln($leftside)$=\ln$(rightside).
So:
$$\ln(1,0877^{x-20}) = \ln(802,8)$$
Apply log-rule: $log_a(x^b) = b\cdot log_a(x)$ on $1,0877^{x-20}$: $\ln(1,0877^{x-20}) = (x-20)\cdot \ln(1,0877)$
We then get
$$(x-20)\cdot \ln(1,0877) = \ln(802,8)$$
Move $\ln(1,0877)$ to right hand side:
$$x-20 = \frac{\ln(802,8)}{\ln(1,0877)}$$
Move $-20$ to right side to get x:
$$x = \frac{\ln(802,8)}{\ln(1,0877)} + 20$$
$x$'s real solution is more approximately equal to $99,5584$
thats also close to a hundred:
$$x \approx 100$$
From your original equation: $10000\cdot 1,0877^{x-20}=8028000$ we can check if the right-hand side is close to $8028000$.
To check the validity of the real solution we can plug in the closest value we found for $x$:
First set $x=99,5584$.
$$10000\cdot 1,0877^{99,5584-20} =$$
$$10000\cdot 1,0877^{79,5584} =$$
$$8028009.0145...$$
which is close to $8028000$, and $x$'s approximation is close.
