What is the answer to ((16)/(4^x))=8-4^x ?

The answer to ((16)/(4^x))=8-4^x is x=1

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((16)/(4^x))=8-4^x

(\frac{16}{4 ^{x}}) = 8 - 4^{x}

x = 1

Solution steps

(\frac{16}{4 ^{x}}) = 8 - 4^{x}

Apply exponent rules

16 (4^{x})^{- 1} = 8 - 4^{x}

Rewrite the equation with

4^{x} = u

16 (u)^{- 1} = 8 - u

Solve

16 u^{- 1} = 8 - u : u = 4

u = 4

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 4 : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

e^{2 x} + 3 e^{x} = 0

6^{x} = 3^{x + 5}

2 5^{2 x} = 5^{x^{2} - 12}

0. 5^{\frac{x}{10}} = 0.125

4 9^{x + 1} = 7

What is the answer to ((16)/(4^x))=8-4^x ?
The answer to ((16)/(4^x))=8-4^x is x=1
Solve for x: ((16)/(4^x))=8-4^x
The solution is x=1