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Popular >

4^x-2=2^6x

Solution

4^{x} - 2 = 2^{6} x

Solution

x = - \frac{16 W _{- 1} ( - \frac{l n ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} ) + ln ( 2 )}{32 ln ( 2 )}, x = - \frac{16 W _{0} ( - \frac{l n ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} ) + ln ( 2 )}{32 ln ( 2 )}

+1

Decimal Notation

x = 4.00683 \dots, x = - 0.01596 \dots

Solution steps

4^{x} - 2 = 2^{6} x

Prepare

4^{x} - 2 = 2^{6} x

for Lambert form:

1 = e^{- 2 l n (2) x} (64 x + 2)

Rewrite the equation with

2 ln (2) (- x - \frac{1}{32}) = u

and

x = - \frac{16 u + ln ( 2 )}{32 ln ( 2 )}

1 = e^{- 2 l n (2) (- \frac{16 u + l n ( 2 )}{32 l n ( 2 )})} (64 (- \frac{16 u + ln ( 2 )}{32 ln ( 2 )}) + 2)

Simplify

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

Rewrite

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

in Lambert form:

\frac{e ^{\frac{16 u + l n ( 2 )}{16}} u}{e ^{\frac{l n ( 2 )}{16}}} = - \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}}

Solve

\frac{e ^{\frac{16 u + l n ( 2 )}{16}} u}{e ^{\frac{l n ( 2 )}{16}}} = - \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} : u = W_{- 1} (- \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}}), u = W_{0} (- \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}})

u = W_{- 1} (- \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}}), u = W_{0} (- \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}})

Substitute back

u = 2 ln (2) (- x - \frac{1}{32}),

solve for

x

Solve

2 ln (2) (- x - \frac{1}{32}) = W_{- 1} (- \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}}) : x = - \frac{16 W _{- 1} ( - \frac{l n ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} ) + ln ( 2 )}{32 ln ( 2 )}

Solve

2 ln (2) (- x - \frac{1}{32}) = W_{0} (- \frac{ln ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}}) : x = - \frac{16 W _{0} ( - \frac{l n ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} ) + ln ( 2 )}{32 ln ( 2 )}

x = - \frac{16 W _{- 1} ( - \frac{l n ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} ) + ln ( 2 )}{32 ln ( 2 )}, x = - \frac{16 W _{0} ( - \frac{l n ( 2 )}{32 e ^{\frac{l n ( 2 )}{16}}} ) + ln ( 2 )}{32 ln ( 2 )}

Popular Examples

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2^{(x+2)(x^2-5x+6)}=1

2^{(x + 2) (x^{2} - 5 x + 6)} = 1

16(2.9)^x=(6.4)^x

16 (2.9)^{x} = (6.4)^{x}

5^{x} = \frac{1}{125}

solvefor n,a=p(1+i)^n solve for

n, a = p (1 + i)^{n}

Frequently Asked Questions (FAQ)

What is the answer to 4^x-2=2^6x ?
The answer to 4^x-2=2^6x is
Solve for x: 4^x-2=2^6x
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