Solve 2^(3x)=4^(x+2)

Question

Please solve.

Answer 1

To solve this equation, manipulate the numbers so that the base numbers are the same. Since 4 = 2^2 we can rewrite this as:

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

Expanding the exponent gives:

2^3x = 2^(2x+4)

Now that both bases are the same, we see that

3x = 2x+4

Solving for x, we subtract 2x from both sides to get

x = 4

You can plug in the value of 4 for x in the original equation and see that it is correct.