What is the answer to log_{3}(3^x-6)=x-1 ?

The answer to log_{3}(3^x-6)=x-1 is x=2

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log_{3}(3^x-6)=x-1

lo g_{3} (3^{x} - 6) = x - 1

x = 2

Solution steps

lo g_{3} (3^{x} - 6) = x - 1

f (x) = g (x),

then

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

3^{l o g_{3} (3^{x} - 6)} = 3^{x - 1}

Simplify

3^{l o g_{3} (3^{x} - 6)} : 3^{x} - 6

3^{x} - 6 = 3^{x - 1}

Solve

3^{x} - 6 = 3^{x - 1} : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

8 ln (x^{2}) = x

lo g_{5} (- 9 - 2 x) = 2

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

lo g_{3} (x) + lo g_{3} (x + 6) = 3

2 lo g_{10} (x) - lo g_{10} (x - 6) = 0

What is the answer to log_{3}(3^x-6)=x-1 ?
The answer to log_{3}(3^x-6)=x-1 is x=2
Solve for x: log_{3}(3^x-6)=x-1
The solution is x=2