3^(2x) - 7(3^x) - 18 = 0

Demoy  Levene

Demoy Levene

Answered question

2022-10-16

3^(2x) - 7(3^x) - 18 = 0

Answer & Explanation

nick1337

nick1337

Expert2023-06-17Added 777 answers

To solve the equation 32x7(3x)18=0 for x, we can make a substitution to simplify the equation.
Let's make a substitution: u=3x.
Now, we can rewrite the equation in terms of u:
u27u18=0
To solve this quadratic equation, we can factor it:
(u9)(u+2)=0
Now, we can solve for u:
u9=0oru+2=0
u=9oru=2
Since u=3x, we can substitute back to find the values of x:
3x=9or3x=2
For the equation 3x=9, we can take the logarithm base 3 of both sides:
x=log3(9)
x=2
For the equation 3x=2, there are no real solutions, as 3x is always positive.
Therefore, the solution to the equation 32x7(3x)18=0 is x=2.

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