SOLUTION: there is a question sayins solve for x. and shows 27^2x+1=9^4x

Question 414909: there is a question sayins solve for x. and shows 27^2x+1=9^4x

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If the equation is

then please enclose multiple term exponents in parentheses.

Solving equations where the variable is in an exponent is usually done in one of two ways:

Rewrite both sides as powers of the same number. This cannot be done all the time. But this way is faster/easier when it can be done.
Using logarithms.

Since 27 and 9 are both powers of 3, the first ways is available to us on this equation:

The rule for exponents when raising a power to a power is to multiply the exponents:

which simplifies to:

This equation now says that two powers of 3 are equal. The only way this can be true is if the exponents are equal, too. So:
6x+3 = 8x
This is very easy to solve. Subtracting 6x from each side:
3 = 2x
Dividing by 2 we get:
3/2 = x
This is the solution to your equation.
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