Inverting a Log Function: Resulting in a quadratic equation

Applying the formulaUsing multiple rulesUsing variables
Question 1

\( \frac{1}{\log_x3}\times x^2\log_{\frac{1}{x}}27+4x+6=0 \)

\( x=\text{?} \)

Question 2

\( \frac{1}{\log_{2x}6}\times\log_236=\frac{\log_5(x+5)}{\log_52} \)

\( x=\text{?} \)

Question 3

Find X

\( \frac{1}{\log_{x^4}2}\times x\log_x16+4x^2=7x+2 \)

Examples with solutions for Inverting a Log Function: Resulting in a quadratic equation

Exercise #1

1log⁡x3×x2log⁡1x27+4x+6=0 \frac{1}{\log_x3}\times x^2\log_{\frac{1}{x}}27+4x+6=0

x=? x=\text{?}

Video Solution

Answer

23+223 \frac{2}{3}+\frac{\sqrt{22}}{3}

Exercise #2

1log⁡2x6×log⁡236=log⁡5(x+5)log⁡52 \frac{1}{\log_{2x}6}\times\log_236=\frac{\log_5(x+5)}{\log_52}

x=? x=\text{?}

Video Solution

Answer

1.25 1.25

Exercise #3

Find X

1log⁡x42×xlog⁡x16+4x2=7x+2 \frac{1}{\log_{x^4}2}\times x\log_x16+4x^2=7x+2

Video Solution

Answer

−9+1138 \frac{-9+\sqrt{113}}{8}