Find the logarithm of 4 middot Squareroot 4 middot 3 Squarer

Find the logarithm of (4 middot Squareroot 4 middot 3 Squareroot 4 middot 4 Squareroot 4) base 2. A. 2/3 B. 1.2543 C. 2.8881 D. 3.4150 E. 25/6 F. none of these

Solution

log( 4.(4)^1/2*(4)^1/3*(4)^1/4) base2

( 4.(4)^1/2*(4)^1/3*(4)^1/4) = 2^2*2^1*2^(2/3)*2^(1/2) = 2^(2+1+2/3 +1/2)

= 2^(12+6+4+3)/6

2^(25/6)

Now, log( 4.(4)^1/2*(4)^1/3*(4)^1/4) base2 = log₂(2^25/6) = 25/6(log2/log2) = 25/6

Option E