Logarithm problem, help needed.

Question

ln_xlog_√ee^x = 0.2, Find the value of x.

Answer 1

Do in stages log_√e e^x = ln(e^x)/ln(e^1/2) = x/(1/2) = 2x

ln_x2x = .2

x^.2 = 2x

x = (2x)⁵ = 32x⁵

x⁴ = 1/32

x = 1/(2 * 2^1/4) or 8^1/4/4