What is the answer to 4x*8^x=8 ?

The answer to 4x*8^x=8 is x=(\W_{0}(6ln(2)))/(3ln(2))

Solve for x: 4x*8^x=8

The solution is x=(\W_{0}(6ln(2)))/(3ln(2))

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4 x \cdot 8^{x} = 8

x = \frac{W _{0} ( 6 ln ( 2 ) )}{3 ln ( 2 )}

Decimal Notation

x = 0.58838 \dots

Solution steps

4 x \cdot 8^{x} = 8

Prepare

4 x \cdot 8^{x} = 8

for Lambert form:

4 x e^{3 l n (2) x} = 8

Rewrite the equation with

3 ln (2) x = u

and

x = \frac{u}{3 ln ( 2 )}

4 (\frac{u}{3 ln ( 2 )}) e^{u} = 8

Rewrite

4 (\frac{u}{3 ln ( 2 )}) e^{u} = 8

in Lambert form:

e^{u} u = 6 ln (2)

Solve

e^{u} u = 6 ln (2) : u = W_{0} (6 ln (2))

u = W_{0} (6 ln (2))

Substitute back

u = 3 ln (2) x,

solve for

x

Solve

3 ln (2) x = W_{0} (6 ln (2)) : x = \frac{W _{0} ( 6 ln ( 2 ) )}{3 ln ( 2 )}

x = \frac{W _{0} ( 6 ln ( 2 ) )}{3 ln ( 2 )}

(a + 1)^{(a + 1)} = 9^{4}

6^{x} = a^{\frac{x}{4}}

0.1 = 1 0^{x}

e^{2 x} = - x + 2

7^{3 x - 5} = 49

What is the answer to 4x*8^x=8 ?
The answer to 4x*8^x=8 is x=(\W_{0}(6ln(2)))/(3ln(2))
Solve for x: 4x*8^x=8
The solution is x=(\W_{0}(6ln(2)))/(3ln(2))