What is the answer to 5\times 4^x+216\times 4^{-x}=102 ?

The answer to 5\times 4^x+216\times 4^{-x}=102 is x=(ln(18))/(2ln(2)),x=(ln(12/5))/(2ln(2))

Solve for x: 5\times 4^x+216\times 4^{-x}=102

The solution is x=(ln(18))/(2ln(2)),x=(ln(12/5))/(2ln(2))

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5 \cdot 4^{x} + 216 \cdot 4^{- x} = 102

x = \frac{ln ( 18 )}{2 ln ( 2 )}, x = \frac{ln ( \frac{12}{5} )}{2 ln ( 2 )}

Decimal Notation

x = 2.08496 \dots, x = 0.63151 \dots

Solution steps

5 \cdot 4^{x} + 216 \cdot 4^{- x} = 102

Apply exponent rules

5 \cdot 4^{x} + 216 (4^{x})^{- 1} = 102

Rewrite the equation with

4^{x} = u

5 u + 216 (u)^{- 1} = 102

Solve

5 u + 216 u^{- 1} = 102 : u = 18, u = \frac{12}{5}

u = 18, u = \frac{12}{5}

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 18 : x = \frac{ln ( 18 )}{2 ln ( 2 )}

Solve

4^{x} = \frac{12}{5} : x = \frac{ln ( \frac{12}{5} )}{2 ln ( 2 )}

x = \frac{ln ( 18 )}{2 ln ( 2 )}, x = \frac{ln ( \frac{12}{5} )}{2 ln ( 2 )}

2^{x} = 38

e^{6 x} = 7

9^{x} + 3^{x + 3} = 28

2^{n} = 128

2 7^{1 - x} = \frac{1}{81}

What is the answer to 5\times 4^x+216\times 4^{-x}=102 ?
The answer to 5\times 4^x+216\times 4^{-x}=102 is x=(ln(18))/(2ln(2)),x=(ln(12/5))/(2ln(2))
Solve for x: 5\times 4^x+216\times 4^{-x}=102
The solution is x=(ln(18))/(2ln(2)),x=(ln(12/5))/(2ln(2))