What is the answer to 3^{2x+1}+3=10*3^x ?

The answer to 3^{2x+1}+3=10*3^x is x=1,x=-1

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3^{2x+1}+3=10*3^x

3^{2 x + 1} + 3 = 10 \cdot 3^{x}

x = 1, x = - 1

Solution steps

3^{2 x + 1} + 3 = 10 \cdot 3^{x}

Apply exponent rules

(3^{x})^{2} \cdot 3^{1} + 3 = 10 \cdot 3^{x}

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{1} + 3 = 10 u

Solve

u^{2} \cdot 3^{1} + 3 = 10 u : u = 3, u = \frac{1}{3}

u = 3, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = \frac{1}{3} : x = - 1

x = 1, x = - 1

e^{3 x + 1} = 100

5 = 6^{x}

ln (e^{x}) = 1

2 e^{3 x} = 4 e^{5 x}

4^{x} - 10 \cdot 2^{x} + 16 = 0

What is the answer to 3^{2x+1}+3=10*3^x ?
The answer to 3^{2x+1}+3=10*3^x is x=1,x=-1
Solve for x: 3^{2x+1}+3=10*3^x
The solution is x=1,x=-1