What is the answer to 9^x=100 ?

The answer to 9^x=100 is x=(ln(10))/(ln(3))

The solution is x=(ln(10))/(ln(3))

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9^x=100

9^{x} = 100

x = \frac{ln ( 10 )}{ln ( 3 )}

Decimal

x = 2.09590 \dots

Solution steps

9^{x} = 100

Apply exponent rules

x ln (9) = ln (100)

Solve

x ln (9) = ln (100) : x = \frac{ln ( 10 )}{ln ( 3 )}

x = \frac{ln ( 10 )}{ln ( 3 )}

(\frac{1}{5})^{x} \times 12 5^{x + 1} = 4

(\frac{1}{2})^{4 x - 2} = 2^{x - 2}

1 8^{2 x} \cdot 3^{- 2 x} = 6

2^{- 3 n} \cdot \frac{1}{4} = 2^{n + 2}

e^{- x} = 0.5