How do you solve 9^x=3^40?

We have 9 = 3^2;

Then, 9^x = (3^2) ^x = 3^ (2x);

We solve 3^ (2x) = 3^40;

2x = 40;

x = 20 : 2;

x = 10;

Answer: x = 20

Step-by-step explanation:

Manipulate the bases so they are the same, then set the exponents equal to each other and solve for x:

9ˣ = 3⁴⁰

(3²) ˣ = 3⁴⁰

3²ˣ = 3⁴⁰

2x = 40

x = 20