Please help me to answer this!

Question

Solve the equation:

log₃(3^x+1− 54√3)= x

*The answer is : x= 7⁄2

Answer 1

Sure it is. Work it through like this:

Use each side of the equation as the exponent of 3 and you get

3^x+1 - 2*3^3.5 = 3^x

Now divide by 3^x to get 3 - 2*3^3.5-x = 1

and 2 = 2*^3.5-x

1 = 3^3.5-x

and there is your answer!