What is the answer to log_{3}(10+3^{-x})=x ?

The answer to log_{3}(10+3^{-x})=x is x=(ln(5+sqrt(26)))/(ln(3))

Solve for x: log_{3}(10+3^{-x})=x

The solution is x=(ln(5+sqrt(26)))/(ln(3))

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lo g_{3} (10 + 3^{- x}) = x

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

Decimal Notation

x = 2.10487 \dots

Solution steps

lo g_{3} (10 + 3^{- x}) = x

f (x) = g (x),

then

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

3^{l o g_{3} (10 + 3^{- x})} = 3^{x}

Simplify

3^{l o g_{3} (10 + 3^{- x})} : 10 + 3^{- x}

10 + 3^{- x} = 3^{x}

Solve

10 + 3^{- x} = 3^{x} : x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

Verify Solutions:

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

True

The solution is

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

lo g_{10} (C) = 4.4054

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

ln (\frac{18}{x}) = 4

\frac{1}{2} lo g_{10} (x + 4) = 0

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

What is the answer to log_{3}(10+3^{-x})=x ?
The answer to log_{3}(10+3^{-x})=x is x=(ln(5+sqrt(26)))/(ln(3))
Solve for x: log_{3}(10+3^{-x})=x
The solution is x=(ln(5+sqrt(26)))/(ln(3))