What is the answer to log_{3}(3^x-8)=2-x ?

The answer to log_{3}(3^x-8)=2-x is x=2

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log_{3}(3^x-8)=2-x

lo g_{3} (3^{x} - 8) = 2 - x

x = 2

Solution steps

lo g_{3} (3^{x} - 8) = 2 - x

f (x) = g (x),

then

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

3^{l o g_{3} (3^{x} - 8)} = 3^{2 - x}

Simplify

3^{l o g_{3} (3^{x} - 8)} : 3^{x} - 8

3^{x} - 8 = 3^{2 - x}

Solve

3^{x} - 8 = 3^{2 - x} : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{10} (x^{3}) = \frac{1}{2}

lo g_{10} (x) + lo g_{10} (x + 2) = lo g_{10} (3 x)

lo g_{3} (1 + x) + lo g_{3} (x + 3) = 1

2 lo g_{10} (9 - 2 x) = (3 - x)

lo g_{10} (5 x + 1) = 2 + lo g_{10} (2 x - 3)

What is the answer to log_{3}(3^x-8)=2-x ?
The answer to log_{3}(3^x-8)=2-x is x=2
Solve for x: log_{3}(3^x-8)=2-x
The solution is x=2