What is the answer to 9^{x+1}+1=10(3x) ?

The answer to 9^{x+1}+1=10(3x) is No Solution for x\in\mathbb{R}

Solve for x: 9^{x+1}+1=10(3x)

The solution is No Solution for x\in\mathbb{R}

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9^{x + 1} + 1 = 10 (3 x)

No Solution for x \in R

Solution steps

9^{x + 1} + 1 = 10 (3 x)

Prepare

9^{x + 1} + 1 = 10 (3 x)

for Lambert form:

1 = (30 x - 1) e^{2 l n (3) (- x - 1)}

Rewrite the equation with

2 ln (3) (- x + \frac{1}{30}) = u

and

x = - \frac{15 u - ln ( 3 )}{30 ln ( 3 )}

1 = (30 (- \frac{15 u - ln ( 3 )}{30 ln ( 3 )}) - 1) e^{2 l n (3) (- (- \frac{15 u - l n ( 3 )}{30 l n ( 3 )}) - 1)}

Simplify

1 = e^{\frac{15 u - l n ( 3 )}{15} - 2 l n (3)} (- \frac{15 u - ln ( 3 )}{ln ( 3 )} - 1)

Rewrite

1 = e^{\frac{15 u - l n ( 3 )}{15} - 2 l n (3)} (- \frac{15 u - ln ( 3 )}{ln ( 3 )} - 1)

in Lambert form:

e^{u} u = - \frac{e ^{\frac{31 l n ( 3 )}{15}} ln ( 3 )}{15}

Solve

e^{u} u = - \frac{e ^{\frac{31 l n ( 3 )}{15}} ln ( 3 )}{15} :

No Solution for

u \in R

No Solution for x \in R

5^{x - 3} = 625

e^{- x} = - e^{x}

3000000 = 1.0 4^{x}

(7^{3})^{5} = 1680 7^{x}

3^{x} + 3^{2 - x} = 11

What is the answer to 9^{x+1}+1=10(3x) ?
The answer to 9^{x+1}+1=10(3x) is No Solution for x\in\mathbb{R}
Solve for x: 9^{x+1}+1=10(3x)
The solution is No Solution for x\in\mathbb{R}