What is the answer to 10*(0.5)^x-2^3-x=64 ?

The answer to 10*(0.5)^x-2^3-x=64 is x=(\W_{0}(10ln(2)*2^{72}))/(ln(2))-72

Solve for x: 10*(0.5)^x-2^3-x=64

The solution is x=(\W_{0}(10ln(2)*2^{72}))/(ln(2))-72

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10 \cdot (0.5)^{x} - 2^{3} - x = 64

x = \frac{W _{0} ( 10 ln ( 2 ) \cdot 2 ^{72} )}{ln ( 2 )} - 72

Decimal Notation

x = - 2.79096 \dots

Solution steps

10 (0.5)^{x} - 2^{3} - x = 64

Prepare

10 \cdot (0.5)^{x} - 2^{3} - x = 64

for Lambert form:

10 = e^{l n (2) x} (x + 72)

Rewrite the equation with

(x + 72) ln (2) = u

and

x = \frac{u}{ln ( 2 )} - 72

10 = e^{l n (2) (\frac{u}{l n ( 2 )} - 72)} ((\frac{u}{ln ( 2 )} - 72) + 72)

Simplify

10 = \frac{e ^{u - 72 l n (2)} u}{ln ( 2 )}

Rewrite

10 = \frac{e ^{u - 72 l n (2)} u}{ln ( 2 )}

in Lambert form:

e^{u} u = 10 ln (2) \cdot 2^{72}

Solve

e^{u} u = 10 ln (2) \cdot 2^{72} : u = W_{0} (10 ln (2) \cdot 2^{72})

u = W_{0} (10 ln (2) \cdot 2^{72})

Substitute back

u = (x + 72) ln (2),

solve for

x

Solve

(x + 72) ln (2) = W_{0} (10 ln (2) \cdot 2^{72}) : x = \frac{W _{0} ( 10 ln ( 2 ) \cdot 2 ^{72} )}{ln ( 2 )} - 72

x = \frac{W _{0} ( 10 ln ( 2 ) \cdot 2 ^{72} )}{ln ( 2 )} - 72

3^{x} + 3^{x} = 54

4 x = 2^{x}

x, [t] = [p^{x} \cdot d^{y} \cdot e^{2}]

5^{6 x + 8} = 12 5^{4}

(- 4)^{x} = 1024

What is the answer to 10*(0.5)^x-2^3-x=64 ?
The answer to 10*(0.5)^x-2^3-x=64 is x=(\W_{0}(10ln(2)*2^{72}))/(ln(2))-72
Solve for x: 10*(0.5)^x-2^3-x=64
The solution is x=(\W_{0}(10ln(2)*2^{72}))/(ln(2))-72