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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