9^x + 9 = 10*3^x

Answer 1

To solve this equation, we can first simplify it:

9^x + 9 = 10*3^x

We can rewrite 9 as 3^2:

(3^2)^x + 9 = 10*3^x

Now, apply the power rule for exponents (a^m)^n = a^(m*n):

3^(2x) + 9 = 10*3^x

Now we can rewrite 9 as 3^2:

3^(2x) + 3^2 = 10*3^x

Now we have a common base of 3. We can rewrite the equation as:

3^(2x) + 9 = 10*3^x

Since the bases are the same, the exponents must also be equal:

2x = x + 1

Now we can solve for x by subtracting x from both sides:

x = 1

Therefore, the solution to the equation 9^x + 9 = 10*3^x is x = 1.