Question

find the domain of the exponential and logarithmic equations and solve thempls help

Answer 1

Solution

We can start taking common factor in both sides and we got:

$3^x(1+3+3^2)=2^x(1+2^2+2^3)^{}$

and we can simplify like this:

$3^x(13)=2^x(13)^{}$

We can cancel the 13 in both sides and we got:

$3^x=2^x^{}$

Then we can do this using exponentials:

$3^x-2^x=0^{}$

We got:

$x\ln (3)=x\ln (2)$

then the only possible solution would be:

x=0