What is the answer to 16^p+4^{p-1}= 1/(4^3) ?

The answer to 16^p+4^{p-1}= 1/(4^3) is p=(ln((-1+sqrt(2))/8))/(2ln(2))

Solve for p: 16^p+4^{p-1}= 1/(4^3)

The solution is p=(ln((-1+sqrt(2))/8))/(2ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1 6^{p} + 4^{p - 1} = \frac{1}{4 ^{3}}

p = \frac{ln ( \frac{- 1 + 2}{8} )}{2 ln ( 2 )}

Decimal Notation

p = - 2.13577 \dots

Solution steps

1 6^{p} + 4^{p - 1} = \frac{1}{4 ^{3}}

Apply exponent rules

(4^{p})^{2} = \frac{1}{64} - 4^{p} \cdot 4^{- 1}

Rewrite the equation with

4^{p} = u

(u)^{2} = \frac{1}{64} - u \cdot 4^{- 1}

Solve

u^{2} = \frac{1}{64} - u \cdot 4^{- 1} : u = \frac{- 1 + 2}{8}, u = - \frac{1 + 2}{8}

u = \frac{- 1 + 2}{8}, u = - \frac{1 + 2}{8}

Substitute back

u = 4^{p},

solve for

p

Solve

4^{p} = \frac{- 1 + 2}{8} : p = \frac{ln ( \frac{- 1 + 2}{8} )}{2 ln ( 2 )}

Solve

4^{p} = - \frac{1 + 2}{8} :

No Solution for

p \in R

p = \frac{ln ( \frac{- 1 + 2}{8} )}{2 ln ( 2 )}

74 = 1 0^{2.37 x}

t, x^{4 a} = b^{t}

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

a, 1 = \frac{e ^{- a}}{b}

1.0 4^{x} = 5

What is the answer to 16^p+4^{p-1}= 1/(4^3) ?
The answer to 16^p+4^{p-1}= 1/(4^3) is p=(ln((-1+sqrt(2))/8))/(2ln(2))
Solve for p: 16^p+4^{p-1}= 1/(4^3)
The solution is p=(ln((-1+sqrt(2))/8))/(2ln(2))