What is the answer to log_{27}(81^x)=x-1 ?

The answer to log_{27}(81^x)=x-1 is x=-3

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log_{27}(81^x)=x-1

lo g_{27} (8 1^{x}) = x - 1

x = - 3

Solution steps

lo g_{27} (8 1^{x}) = x - 1

f (x) = g (x),

then

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

2 7^{l o g_{27} (8 1^{x})} = 2 7^{x - 1}

Simplify

2 7^{l o g_{27} (8 1^{x})} : 8 1^{x}

8 1^{x} = 2 7^{x - 1}

Solve

8 1^{x} = 2 7^{x - 1} : x = - 3

x = - 3

Verify Solutions:

x = - 3

True

The solution is

x = - 3

ln (x + 3) - ln (4 - 3 x) = 2 ln (2)

lo g_{10} (x) + lo g_{10} (x + 5) = 9

ln (x) = 3 ln (x)

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

ln (x^{2} - 4) = 0

What is the answer to log_{27}(81^x)=x-1 ?
The answer to log_{27}(81^x)=x-1 is x=-3
Solve for x: log_{27}(81^x)=x-1
The solution is x=-3