Hard Logarithm Problems With Solutions: Pdf

Equation: (\frac{\ln 2}{\ln x} \cdot \frac{\ln 2}{\ln(2x)} = \frac{\ln 2}{\ln(4x)}).

So (\ln x = \pm \ln(2^{\sqrt{2}})) ⇒ (x = 2^{\sqrt{2}}) or (x = 2^{-\sqrt{2}}). hard logarithm problems with solutions pdf

Equation: (\ln 2 \cdot (a + 2\ln 2) = a \cdot (a + \ln 2)). Equation: (\frac{\ln 2}{\ln x} \cdot \frac{\ln 2}{\ln(2x)} =

Cancel (a\ln 2) both sides: (2(\ln 2)^2 = a^2 \Rightarrow a = \pm \sqrt{2} \ln 2). (\log_3 x = \frac{t}{\ln 3})

Convert to base 10 (or natural log): Let (\ln x = t). (\log_2 x = \frac{t}{\ln 2}), (\log_3 x = \frac{t}{\ln 3}), (\log_4 x = \frac{t}{\ln 4} = \frac{t}{2\ln 2}).