Hi there, if someone could please help me solve this problem I'd be most grateful:
2^x-3 . 5^x+1 = 62.5
I am unsure of how your problem reads, but I think it is this...Please use () in the future.
$\displaystyle 2^{x-3}\cdot 5^{x+1}=62.5$ First multiply both sides by $\displaystyle 2^4=16$
This gives
$\displaystyle 2^{x+1}\cdot 5^{x+1}=1000$ Now since the exponents on the left hand side are the same we can combine the bases to get
$\displaystyle 10^{x+1}=1000 \iff 10^{x+1}=10^{3} \implies x+1=3 \implies x=2$