What is the value of #x# if #2^3(3^(2x + 3)) = 6(2)^2#?

1 Answer
Dec 21, 2016

Answer:

#x = -1#

Explanation:

Isolate the exponent.

#3^(2x + 3) = 24/8#

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

We are in common bases--logarithms are not necessary.

#2x + 3 = 1#

#2x = -2#

#x = -1#

Check back in the original equation:

#8(3^(2(-1) + 3)) =^? 24#

#8(3^1) = 24" "color(green)(√)#

Practice Exercises

  1. Solve each equation by writing in equivalent bases and using laws of exponents.

a) #3^(2x+ 5) = 9^(x - 2)#

b) #2^(5x + 1)/16^(3x) = 8^(4x + 2)#

Hopefully this helps!