Circle the value of the logarithm of 5 Squareroot 2 middot4S

Circle the value of the logarithm of (^5 Squareroot 2 middot^4Squareroot2 middot^3Squareroot2 middot Squareroot2) base -1.4534 1/1920 0.3863 77/120 0 8895 none of these

Solution

We will use the change of base formula for logatithms i.e. log_ax = log_bx/log_b a   and the formula log p^q =   qlog p.

log₄ [2^1/5.2^1/4 .2^1/3. 2^1/2] = log₄(2^77/60)=(77/60)log₄(2)=(77/60)log₁₀(2)/log₁₀(4) = (77/60) log₁₀(2)/ 2log₁₀(2) = 77/120 ( as 4 = 2²). Thus, the answer D is correct.