What is the answer to 3^{1+2x}=23+(36)/(3^{2x)} ?

The answer to 3^{1+2x}=23+(36)/(3^{2x)} is x=1

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3^{1+2x}=23+(36)/(3^{2x)}

3^{1 + 2 x} = 23 + \frac{36}{3 ^{2 x}}

x = 1

Solution steps

3^{1 + 2 x} = 23 + \frac{36}{3 ^{2 x}}

Apply exponent rules

(3^{x})^{2} \cdot 3^{1} = 23 + 36 (3^{x})^{- 2}

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{1} = 23 + 36 (u)^{- 2}

Solve

u^{2} \cdot 3^{1} = 23 + 36 u^{- 2} : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = - 3 :

No Solution for

x \in R

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

e^{2 l n (x)} = 16

3^{x - 1} + 3^{1 + x} - 3^{x} = 63

5^{x^{2}} \cdot 5^{4} = 5^{5 x}

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

27 (3^{2 x}) + 134 (3^{x}) - 5 = 0

What is the answer to 3^{1+2x}=23+(36)/(3^{2x)} ?
The answer to 3^{1+2x}=23+(36)/(3^{2x)} is x=1
Solve for x: 3^{1+2x}=23+(36)/(3^{2x)}
The solution is x=1