What is the answer to 6^x+4(6^{-x})=5 ?

The answer to 6^x+4(6^{-x})=5 is x=(2ln(2))/(ln(6)),x=0

Solve for x: 6^x+4(6^{-x})=5

The solution is x=(2ln(2))/(ln(6)),x=0

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6^{x} + 4 (6^{- x}) = 5

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

Decimal Notation

x = 0.77370 \dots, x = 0

Solution steps

6^{x} + 4 (6^{- x}) = 5

Apply exponent rules

6^{x} + 4 (6^{x})^{- 1} = 5

Rewrite the equation with

6^{x} = u

u + 4 (u)^{- 1} = 5

Solve

u + 4 u^{- 1} = 5 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 4 : x = \frac{2 ln ( 2 )}{ln ( 6 )}

Solve

6^{x} = 1 : x = 0

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

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

2^{9} = 2^{3 x}

1 0^{x + 2} = 5

e^{3 - 4 x} = 7

1 0^{l o g_{10} (x^{2} + x)} = 20

What is the answer to 6^x+4(6^{-x})=5 ?
The answer to 6^x+4(6^{-x})=5 is x=(2ln(2))/(ln(6)),x=0
Solve for x: 6^x+4(6^{-x})=5
The solution is x=(2ln(2))/(ln(6)),x=0