Question

can someone PLEASE HELP me SIMPLIFY this problem (2^x/2)^2+ 〖log〗_3 (2x)+ 2〖log〗_3 (2x)

Answer 1

\[2^{x} + 3\log_{3} 2x\]

Answer 2

\[(2^{x}/2)^{2}+ \log_3 (2x)+ 2\log_3 (2x)\]

Answer 3

yes thats the problem abtrehearn

Answer 4

\[= 2^{x} + \log_3(2x) + \log_3((2x )^{2})\]
\[= 2^{x} + \log_3((2x)^{3})\]
\[= 2^{x} + \log_3(8) + 3 \log_3(x)\]

Answer 5

We can change the base of the logarithmic terms from 3 to 2.

Answer 6

\[\log_3(8) + 3 \log_3(x)= \log_2(8)/\log_2(3) + 3 \log_2(x)/\log_2(3)\]

Answer 7

ok

Answer 8

\[3(1 + \log_2(x))/\log_2(3).\]

Answer 9

That makes the answer
\[2^{x} + 3(1 + \log_2(x))/\log_2(3).\]