Question

If logₑ 2. logₓ27 = log₁₀ 8. logₑ 10, then x (a) 1 (b) 3 (c) 2 (d) 4

Answer 1

Answer:

$log_{e}(2) . log_{x}(27) = log_{10}(8) log_{e}(10) \\ = > log_{e}(2) . log_{10}(e) = log_{10}8. log_{27}(x) \\ = > log_{10}(2) . log_{8}(10) = log_{27}(x) \\ = > log_{8}(2) = \frac{1}{3} = log_{27}(x) \\ = > x^{ \frac{1}{3} } = 27 \\ = > x = \sqrt[3]{27} = 3$