Question

What is the solution to the equation log4 x + log 4 2 =3

i did x*2 = 3
2x = 3
x= 3/2
but my options are

x=1/2
x=2
x=32
x=128

Answer 1

\[ log_4(x) + log_4(2)= 3\]
add logs is the same as multiplying and then taking the log
\[ log_4(2x) = 3\]
now make each side the exponent of 4
\[ 4^{log_4(2x)} = 4^3 \]
the ugly stuff on the left turns into 2x
(you should learn that this is how you "undo" a log)
now solve for x
\[ 2x= 4^3\]
\[ x= \frac{1}{2}\cdot 64 \]

Answer 2

32 :-)