What is the answer to log_{3}(9^x-2)=x ?

The answer to log_{3}(9^x-2)=x is x=(ln(2))/(ln(3))

Solve for x: log_{3}(9^x-2)=x

The solution is x=(ln(2))/(ln(3))

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lo g_{3} (9^{x} - 2) = x

x = \frac{ln ( 2 )}{ln ( 3 )}

Solution steps

lo g_{3} (9^{x} - 2) = x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

3^{l o g_{3} (9^{x} - 2)} = 3^{x}

Simplify

3^{l o g_{3} (9^{x} - 2)} : 9^{x} - 2

9^{x} - 2 = 3^{x}

Solve

9^{x} - 2 = 3^{x} : x = \frac{ln ( 2 )}{ln ( 3 )}

x = \frac{ln ( 2 )}{ln ( 3 )}

Verify Solutions:

x = \frac{ln ( 2 )}{ln ( 3 )}

True

The solution is

x = \frac{ln ( 2 )}{ln ( 3 )}

lo g_{2} (5 - 3 x) = 1

2 \cdot lo g_{4} (3 x) = 3

lo g_{8} (x) + lo g_{7} (x) = 1

0 = ln (x^{2})

lo g_{3} (x) - lo g_{9} (x) = 1

What is the answer to log_{3}(9^x-2)=x ?
The answer to log_{3}(9^x-2)=x is x=(ln(2))/(ln(3))
Solve for x: log_{3}(9^x-2)=x
The solution is x=(ln(2))/(ln(3))