What is the answer to 4^x=2^{x+1}+3 ?

The answer to 4^x=2^{x+1}+3 is x=(ln(3))/(ln(2))

Solve for x: 4^x=2^{x+1}+3

The solution is x=(ln(3))/(ln(2))

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4^{x} = 2^{x + 1} + 3

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

Decimal Notation

x = 1.58496 \dots

Solution steps

4^{x} = 2^{x + 1} + 3

Apply exponent rules

(2^{x})^{2} = 2^{x} \cdot 2^{1} + 3

Rewrite the equation with

2^{x} = u

(u)^{2} = u \cdot 2^{1} + 3

Solve

u^{2} = u \cdot 2^{1} + 3 : u = 3, u = - 1

u = 3, u = - 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 3 : x = \frac{ln ( 3 )}{ln ( 2 )}

Solve

2^{x} = - 1 :

No Solution for

x \in R

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

(7)^{- 1} \cdot (7)^{3 k + 2} = \frac{( 7 ) ^{15}}{( ( 7 ) ^{8} )}

9^{n + 1} - 9^{n} = 72

x, (\frac{x}{10}) - a \cdot e^{- \frac{x}{( r \cdot t )}} = 0

n = 1 + (\frac{9}{10})^{n}

(\frac{3}{5})^{1 - 2 x} = \frac{417}{27}

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