MATH SOLVE

5 months ago

Q:
# x^(logx) = 1000000xFind x.

Accepted Solution

A:

Answer:[tex]x = 1000[/tex] or [tex]x = 0.01[/tex] Step-by-step explanation:We are given a logarithmic equation of x and we have to solve it for x.Given,[tex]x^{\log x} = 1000000x[/tex]β [tex]x^{\log x} = 10^{6} \times x[/tex]Now, taking log on both sides, we get[tex]\log x^{\log x} = \log 10^{6} \times x[/tex]β [tex]\log x .\log x = \log 10^{6} Β + \log x[/tex]{Since [tex]\log a^{b} = b\log a[/tex] and [tex]\log ab = \log a + \log b[/tex]}β [tex](\log x)^{2} = 6 + \log x[/tex]{Since log 10 = 1}β aΒ² = 6 + a {Where, a = log x}β aΒ² - a - 6 = 0β (a - 3)(a + 2) = 0β a = 3 or a = -2β [tex]\log x = 3[/tex] or [tex]\log x = - 2[/tex]Now, converting logarithm to exponential form, we get,β [tex]x = 10^{3} = 1000[/tex] or [tex]x = 10^{- 2} = \frac{1}{100} = 0.01[/tex] (Answer)