What is the answer to 3^{m-1}+3^m-12=0 ?

The answer to 3^{m-1}+3^m-12=0 is m=2

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3^{m-1}+3^m-12=0

3^{m - 1} + 3^{m} - 12 = 0

m = 2

Solution steps

3^{m - 1} + 3^{m} - 12 = 0

Factor

3^{m - 1} + 3^{m} - 12 : \frac{4}{3} (3^{m} - 9)

\frac{4}{3} (3^{m} - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3^{m} - 9 = 0

Solve

3^{m} - 9 = 0 : m = 2

m = 2

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3^{2 x + 3} = 5^{3 x + 1}

49 (7^{2 x}) - 344 (7^{x}) + 7 = 0

1 6^{m - 1} = 4^{m + 1}

2^{2 x} - 3 \cdot 2^{x} + 2 = 0