What is the answer to 2(6^x)-54(2^x)-16(3^x)+432=0 ?

The answer to 2(6^x)-54(2^x)-16(3^x)+432=0 is x=3,x=(ln(3*3^{941/1054}))/(ln(2))

Solve for x: 2(6^x)-54(2^x)-16(3^x)+432=0

The solution is x=3,x=(ln(3*3^{941/1054}))/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2 (6^{x}) - 54 (2^{x}) - 16 (3^{x}) + 432 = 0

x = 3, x = \frac{ln ( 3 \cdot 3 ^{\frac{941}{1054}} )}{ln ( 2 )}

Decimal Notation

x = 3, x = 3.00000 \dots

Solution steps

2 (6^{x}) - 54 (2^{x}) - 16 (3^{x}) + 432 = 0

Apply exponent rules

(2^{x})^{2.58496 \dots} \cdot 2^{1} - 54 \cdot 2^{x} - 16 (2^{x})^{1.58496 \dots} + 432 = 0

Rewrite the equation with

2^{x} = u

(u)^{2.58496 \dots} \cdot 2^{1} - 54 u - 16 (u)^{1.58496 \dots} + 432 = 0

Solve

u^{2.58496 \dots} \cdot 2^{1} - 54 u - 16 u^{1.58496 \dots} + 432 = 0 : u = 8, u = 3 \cdot 3^{\frac{941}{1054}}

u = 8, u = 3 \cdot 3^{\frac{941}{1054}}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 3 \cdot 3^{\frac{941}{1054}} : x = \frac{ln ( 3 \cdot 3 ^{\frac{941}{1054}} )}{ln ( 2 )}

x = 3, x = \frac{ln ( 3 \cdot 3 ^{\frac{941}{1054}} )}{ln ( 2 )}

7^{x + 2} + 7^{x + 1} = 8

12000 = 200 e^{0.01 t}

4^{x} = 81

2^{x - 2} = 4^{2021}

3^{x} + 3^{x + 1} = 36

What is the answer to 2(6^x)-54(2^x)-16(3^x)+432=0 ?
The answer to 2(6^x)-54(2^x)-16(3^x)+432=0 is x=3,x=(ln(3*3^{941/1054}))/(ln(2))
Solve for x: 2(6^x)-54(2^x)-16(3^x)+432=0
The solution is x=3,x=(ln(3*3^{941/1054}))/(ln(2))