What is the answer to 6^x=3^{2x}-2^{2x} ?

The answer to 6^x=3^{2x}-2^{2x} is x=(ln((1+sqrt(5))/2))/(ln(3/2))

Solve for x: 6^x=3^{2x}-2^{2x}

The solution is x=(ln((1+sqrt(5))/2))/(ln(3/2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6^{x} = 3^{2 x} - 2^{2 x}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

Decimal Notation

x = 1.18681 \dots

Solution steps

6^{x} = 3^{2 x} - 2^{2 x}

Divide both sides by

2^{2 x}

\frac{6 ^{x}}{2 ^{2 x}} = \frac{3 ^{2 x}}{2 ^{2 x}} - \frac{2 ^{2 x}}{2 ^{2 x}}

Simplify

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

Apply exponent rules

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

Rewrite the equation with

(\frac{3}{2})^{x} = u

u = (u)^{2} - 1

Solve

u = u^{2} - 1 : u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

Substitute back

u = (\frac{3}{2})^{x},

solve for

x

Solve

(\frac{3}{2})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

Solve

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

No Solution for

x \in R

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

7^{2 x} - 56 \cdot 7^{x} + 343 = 0

4^{x} - 1 6^{x - 2} = 0

\frac{15}{1 + 2 e ^{- 0.5 n}} = 1.8

(2 x - 5)^{x} = (2 x - 5)^{3 x - 4}

x e^{x} + 2 e^{x} = 0

What is the answer to 6^x=3^{2x}-2^{2x} ?
The answer to 6^x=3^{2x}-2^{2x} is x=(ln((1+sqrt(5))/2))/(ln(3/2))
Solve for x: 6^x=3^{2x}-2^{2x}
The solution is x=(ln((1+sqrt(5))/2))/(ln(3/2))