Hard Logarithm Problems With Solutions Pdf Apr 2026

Better: Look for (x) such that each term =1: (\frac{\ln(2x+3)}{\ln x}=1 \Rightarrow 2x+3=x \Rightarrow x=-3) impossible. Second term =1: (\ln(x+2)=\ln(x+1) \Rightarrow x+2=x+1 \Rightarrow 2=1) impossible.

Cancel (a\ln 2) both sides: (2(\ln 2)^2 = a^2 \Rightarrow a = \pm \sqrt{2} \ln 2). hard logarithm problems with solutions pdf

Equation: (\frac{\ln 2}{\ln x} \cdot \frac{\ln 2}{\ln(2x)} = \frac{\ln 2}{\ln(4x)}). Better: Look for (x) such that each term

Challenging Exercises for Advanced High School & Early College Students -\sqrt{6}). Solution 3 Domain: (x&gt

Check domain: all real OK. (x=0, \sqrt{6}, -\sqrt{6}). Solution 3 Domain: (x>0), (x\neq 1), (2x+3>0 \Rightarrow x>-1.5), (x+1>0) and (x+1\neq 1 \Rightarrow x> -1, x\neq 0), plus (x+2>0) (automatic). So (x>0), (x\neq 1).