Question

Can somebody explain to me how they got 3^4(x) = 3^3(x+2)? Then explain what happened to the 3 in 3^4 and the 3 in 3^3? Please and thank you, I don't understand it at all.

Answer 1

x=6

Explanation:

81^x = 27 ^(x+2)

81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation

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

When we have a power to a power we can multiply the exponents

a ^b^c = a^(b*c)

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

Since the bases are the same, the exponents have to be the same

a^b = a^c means b=c

4x = 3(x+2)

Now we can solve for x

Distribute

4x = 3x+6

Subtract 3x from each side

4x-3x = 3x-3x+6

x = 6