What is the answer to x\times 2^{x-1}=32 ?

The answer to x\times 2^{x-1}=32 is x=4

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x\times 2^{x-1}=32

x \cdot 2^{x - 1} = 32

x = 4

Solution steps

x \cdot 2^{x - 1} = 32

Prepare

x \cdot 2^{x - 1} = 32

for Lambert form:

x e^{l n (2) (x - 1)} = 32

Rewrite the equation with

x ln (2) = u

and

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

(\frac{u}{ln ( 2 )}) e^{l n (2) ((\frac{u}{l n ( 2 )}) - 1)} = 32

Simplify

\frac{e ^{u - l n (2)} u}{ln ( 2 )} = 32

Rewrite

\frac{e ^{u - l n (2)} u}{ln ( 2 )} = 32

in Lambert form:

e^{u} u = 64 ln (2)

Solve

e^{u} u = 64 ln (2) : u = 4 ln (2)

u = 4 ln (2)

Substitute back

u = x ln (2),

solve for

x

Solve

x ln (2) = 4 ln (2) : x = 4

x = 4

3^{x + 1} + 3^{x} + 3^{x + 1} = 39

3^{\frac{x}{3}} = 99

5^{x} = 44

3^{3 x} = 3

2^{\frac{x}{4}} = 9

What is the answer to x\times 2^{x-1}=32 ?
The answer to x\times 2^{x-1}=32 is x=4
Solve for x: x\times 2^{x-1}=32
The solution is x=4