What is the answer to 8(3^x)+5(2^x)-6^x=40 ?

The answer to 8(3^x)+5(2^x)-6^x=40 is x=3,x=(665ln(5))/(1054ln(2))

Solve for x: 8(3^x)+5(2^x)-6^x=40

The solution is x=3,x=(665ln(5))/(1054ln(2))

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8 (3^{x}) + 5 (2^{x}) - 6^{x} = 40

x = 3, x = \frac{665 ln ( 5 )}{1054 ln ( 2 )}

Decimal Notation

x = 3, x = 1.46497 \dots

Solution steps

8 (3^{x}) + 5 (2^{x}) - 6^{x} = 40

Apply exponent rules

8 (2^{x})^{1.58496 \dots} + 5 \cdot 2^{x} - (2^{x})^{2.58496 \dots} = 40

Rewrite the equation with

2^{x} = u

8 (u)^{1.58496 \dots} + 5 u - (u)^{2.58496 \dots} = 40

Solve

8 u^{1.58496 \dots} + 5 u - u^{2.58496 \dots} = 40 : u = 8, u = 5^{\frac{665}{1054}}

u = 8, u = 5^{\frac{665}{1054}}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 5^{\frac{665}{1054}} : x = \frac{665 ln ( 5 )}{1054 ln ( 2 )}

x = 3, x = \frac{665 ln ( 5 )}{1054 ln ( 2 )}

2^{x} = x^{2}

e^{x} = 2

3 \cdot 2^{x} = (\frac{1}{3}) \cdot 4^{x}

3^{x} + 9^{x} = 2 7^{x}

4^{x} + 6^{x} = 9^{x}

What is the answer to 8(3^x)+5(2^x)-6^x=40 ?
The answer to 8(3^x)+5(2^x)-6^x=40 is x=3,x=(665ln(5))/(1054ln(2))
Solve for x: 8(3^x)+5(2^x)-6^x=40
The solution is x=3,x=(665ln(5))/(1054ln(2))