Given that 3^x = 9^{y - 1}, show that x = 2y – 2.

Anonymous
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Step 1: Rewrite the problem using the same base.
EXAMPLE: 3^x\ =\ 9^{\left(y-1\right)}
3^x\ =\ \left(3\cdot3\right)^{y-1}
3^{x\ }\ =\ 3^{2\left(y-1\right)}
Step 2: Use the laws of exponents to simplify the equation
NOTE: Since the bases are the same, we can drop the bases and set the exponents equal to each other.
EXAMPLE: 3^{x\ }\ =\ 3^{2\left(y-1\right)}
x\ =\ 2\left(y-1\right)
Step 3: Simplify the equation and verify, is it showing the given equation or not