What is the answer to 4^{(x-2)}=(4x)/(16) ?

The answer to 4^{(x-2)}=(4x)/(16) is x=1,x= 1/2

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4^{(x-2)}=(4x)/(16)

4^{(x - 2)} = \frac{4 x}{16}

x = 1, x = \frac{1}{2}

Decimal Notation

x = 1, x = 0.5

Solution steps

4^{(x - 2)} = \frac{4 x}{16}

Prepare

4^{(x - 2)} = \frac{4 x}{16}

for Lambert form:

16 = e^{2 l n (2) (- x + 3)} x

Rewrite the equation with

- 2 ln (2) x = u

and

x = - \frac{u}{2 ln ( 2 )}

16 = e^{2 l n (2) (- (- \frac{u}{2 l n ( 2 )}) + 3)} (- \frac{u}{2 ln ( 2 )})

Simplify

16 = - \frac{e ^{u + 6 l n (2)} u}{2 ln ( 2 )}

Rewrite

16 = - \frac{e ^{u + 6 l n (2)} u}{2 ln ( 2 )}

in Lambert form:

e^{u} u = - \frac{ln ( 2 )}{2}

Solve

e^{u} u = - \frac{ln ( 2 )}{2} : u = - 2 ln (2), u = - ln (2)

u = - 2 ln (2), u = - ln (2)

Substitute back

u = - 2 ln (2) x,

solve for

x

Solve

- 2 ln (2) x = - 2 ln (2) : x = 1

Solve

- 2 ln (2) x = - ln (2) : x = \frac{1}{2}

x = 1, x = \frac{1}{2}

4^{x - 5} = 32

3^{x + 1} + 3 = 30

4^{x + 4} = 1 6^{3 x - 4}

4^{x - 1} = (2)^{x}

ln (5^{8 x + 5}) = ln (2)

What is the answer to 4^{(x-2)}=(4x)/(16) ?
The answer to 4^{(x-2)}=(4x)/(16) is x=1,x= 1/2
Solve for x: 4^{(x-2)}=(4x)/(16)
The solution is x=1,x= 1/2