What is the value of #x# if #2^3(3^(2x + 3)) = 6(2)^2#?
1 Answer
Dec 21, 2016
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
- Solve each equation by writing in equivalent bases and using laws of exponents.
a)
b)
Hopefully this helps!