Examples with solutions for Power Property of Logorithms: Using multiple rules

Exercise #1

log45+log423log42= \frac{\log_45+\log_42}{3\log_42}=

Video Solution

Answer

log810 \log_810

Exercise #2

log311log34+1ln32log3= \frac{\log_311}{\log_34}+\frac{1}{\ln3}\cdot2\log3=

Video Solution

Answer

log411+loge2 \log_411+\log e^2

Exercise #3

2log78log74+1log43×log29= \frac{2\log_78}{\log_74}+\frac{1}{\log_43}\times\log_29=

Video Solution

Answer

7 7

Exercise #4

3(ln4ln5log57+1log65)= -3(\frac{\ln4}{\ln5}-\log_57+\frac{1}{\log_65})=

Video Solution

Answer

3log5724 3\log_5\frac{7}{24}

Exercise #5

log76log71.53log721log82= \frac{\log_76-\log_71.5}{3\log_72}\cdot\frac{1}{\log_{\sqrt{8}}2}=

Video Solution

Answer

1 1

Exercise #6

log47×log149aclog4b= \frac{\log_47\times\log_{\frac{1}{49}}a}{c\log_4b}=

Video Solution

Answer

logbc1a \log_{b^c}\frac{1}{\sqrt{a}}

Exercise #7

logx16×ln7lnxln4logx49= \log_x16\times\frac{\ln7-\ln x}{\ln4}-\log_x49=

Video Solution

Answer

2 -2

Exercise #8

(2log32+log3x)log23log2x=3x7 (2\log_32+\log_3x)\log_23-\log_2x=3x-7

x=? x=\text{?}

Video Solution

Answer

3 3

Exercise #9

logx4+logx30.25xlogx11+x=3 \frac{\log_x4+\log_x30.25}{x\log_x11}+x=3

x=? x=\text{?}

Video Solution

Answer

2 2

Exercise #10

1log2x6×log236=log5(x+5)log52 \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 #11

Find X

1logx42×xlogx16+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}