What is the answer to log_{6}(3^x)=x^2 ?

The answer to log_{6}(3^x)=x^2 is x=0,x=(ln(3))/(ln(6))

Solve for x: log_{6}(3^x)=x^2

The solution is x=0,x=(ln(3))/(ln(6))

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lo g_{6} (3^{x}) = x^{2}

x = 0, x = \frac{ln ( 3 )}{ln ( 6 )}

Decimal Notation

x = 0, x = 0.61314 \dots

Solution steps

lo g_{6} (3^{x}) = x^{2}

f (x) = g (x),

then

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

6^{l o g_{6} (3^{x})} = 6^{x^{2}}

Simplify

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

3^{x} = 6^{x^{2}}

Solve

3^{x} = 6^{x^{2}} : x = 0, x = \frac{ln ( 3 )}{ln ( 6 )}

x = 0, x = \frac{ln ( 3 )}{ln ( 6 )}

Verify Solutions:

x = 0

True

, x = \frac{ln ( 3 )}{ln ( 6 )}

True

The solutions are

x = 0, x = \frac{ln ( 3 )}{ln ( 6 )}

ln (x) = - 0.5

x, f^{- 1} (x) = ln (x)

x, ln (x) - ln (x - 1) = 1

x, ln (x) - ln (x - 1) = t

lo g_{a} (8) = 2

What is the answer to log_{6}(3^x)=x^2 ?
The answer to log_{6}(3^x)=x^2 is x=0,x=(ln(3))/(ln(6))
Solve for x: log_{6}(3^x)=x^2
The solution is x=0,x=(ln(3))/(ln(6))