Algebra

Logarithmic Functions

Logarithmic Functions: Level 3 Challenges

         

logx(xxxx)=?\large \log_{\sqrt{x}} \left( \sqrt{x\sqrt{x\sqrt{x\sqrt{x}}}} \right) = \, ?

  • Clarification: xx is a positive real number and x1.x \neq 1.

How many digits does the number 21000 2^{1000} contain?

You are given that log102=0.3010\log_{10} 2 = 0.3010 correct up to 4 decimal places.

xlog10x=100x \Large x ^{\log_{10} x } = 100x

How many real solutions are there to the above equation?

{logxw=24logyw=40logxyzw=12\Large\begin{cases} \log_x w & = & 24 \\ \log_y w & = & 40 \\ \log_{xyz} w & = & 12 \end{cases}

If x,y,zx,y,z are real numbers greater than 1 and ww is a positive number satisfying the system above, then find the value of (logwz)1\left (\log_w z \right)^{-1}.

Given that

log2(log8x)=log8(log2x),\log_2(\log_8x)=\log_8(\log_2x),

find the value of (log2x)2(\log_2x)^2.

×

Problem Loading...

Note Loading...

Set Loading...