What is the answer to 9*5^{-x}+5^x=10 ?

The answer to 9*5^{-x}+5^x=10 is x=(2ln(3))/(ln(5)),x=0

Solve for x: 9*5^{-x}+5^x=10

The solution is x=(2ln(3))/(ln(5)),x=0

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9 \cdot 5^{- x} + 5^{x} = 10

x = \frac{2 ln ( 3 )}{ln ( 5 )}, x = 0

Decimal Notation

x = 1.36521 \dots, x = 0

Solution steps

9 \cdot 5^{- x} + 5^{x} = 10

Apply exponent rules

9 (5^{x})^{- 1} + 5^{x} = 10

Rewrite the equation with

5^{x} = u

9 (u)^{- 1} + u = 10

Solve

9 u^{- 1} + u = 10 : u = 9, u = 1

u = 9, u = 1

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 9 : x = \frac{2 ln ( 3 )}{ln ( 5 )}

Solve

5^{x} = 1 : x = 0

x = \frac{2 ln ( 3 )}{ln ( 5 )}, x = 0

8^{9 x - 2} = 64

2^{2 x} = 4^{x}

7^{3 x^{2}} = \frac{1}{4 9 ^{6 x + 4}}

2^{x - 4} = 4 a^{x - 6}

e^{2 k} = 4

What is the answer to 9*5^{-x}+5^x=10 ?
The answer to 9*5^{-x}+5^x=10 is x=(2ln(3))/(ln(5)),x=0
Solve for x: 9*5^{-x}+5^x=10
The solution is x=(2ln(3))/(ln(5)),x=0