Question

If 5x log2 3
+ 3log2 * = 162 then logarithm of x to the base 4 has the value equal to
(B) 1
(C)-1
(D) 3/2
(A) 2​

Answer 1

Answer:

A. 2

Step-by-step explanation:

5x^(Log 2 base 3)+3(Log x base 2)=162

2^(Log 5x base 3)+3^(Log x base 2)=(2^1)×(3^4)

2^(Log 5x base 3)=2^1      

3^(Log x base 2)=3^4

Log 5x base 3=1                Log x base 2=4

5x=3                                     x=2^4

x=3/5                                   x=16 

Log 16 base 4= 2