Question

log 3 root 3 to the base 27 is equal to X​

Answer 1

Step-by-step explanation:

$log_{27}3 \sqrt{3} = x \\ \therefore \: 3 \sqrt{3} = {27}^{x} \\ \therefore \: 3 \times {3}^{ \frac{1}{2} } = {3}^{3x} \\ \therefore \: {3}^{ 1 + \frac{1}{2} } = {3}^{3x} \\ \therefore \: {3}^{ \frac{3}{2} } = {3}^{3x} \\ \frac{3}{2} = 3x \\ \implies \: x = \frac{3}{2 \times 3} \\ \huge \purple{ \boxed{ \implies \: x = \frac{1}{2} }}$