Question

If log 81 - log 3 = loga, then 9⁴loga =
(1) 4
(2) 16
(3) 2
(4) 8​

Answer 1

Step-by-step explanation:

$log81 - log3 = loga \\ log \frac{81}{3} = loga \\ log27 = loga \\ so \: a \: = 27 \\ now \: {4}^{ log_{9}(a) } = {4}^{ log_{9}(27) } = {4 log_{ {3}^{2} } {3}^{3} } \\ = {4}^{ \frac{3}{2} } = {2}^{2 \times \frac{3}{2} } = {2}^{3} = 8$