Question

Sqrt(2^x) * sqrt(3^x) = 36

Answer 1

2^(x/2) * 3^(x/2) = 36
(2*3)^(x/2) = 36
6^(x/2) = 36
x/2 = 2
х = 4

Answer 2

We can simplify the left side of the equation by using the properties of exponents and square roots:

sqrt(2^x) * sqrt(3^x) = sqrt((2^x) * (3^x)) = sqrt((2 * 3)^x) = sqrt(6^x)

Therefore, the equation can be rewritten as:

sqrt(6^x) = 36

We can solve for x by squaring both sides of the equation:

6^x = 36^2

6^x = 1296

Taking the logarithm of both sides with base 6:

x = log6(1296)

We can simplify this expression by recognizing that 6^4 = 1296:

x = log6(6^4) = 4

Therefore, the solution to the equation is x = 4.