Rules of Logarithms Combined: Using multiple rules

$\log7x+\log(x+1)-\log7=\log2x-\log x$

$?=x$

$1$

$\log4x+\log2-\log9=\log_24$

?=x

$112.5$

$\log_9e^3\times(\log_224-\log_28)(\ln8+\ln2)$

$6$

$\frac{\log_45+\log_42}{3\log_42}=$

$\log_810$

$\log_64\times\log_9x=(\log_6x^2-\log_6x)(\log_92.5+\log_91.6)$

For all 0 < x

Calculate the value of the following expression:

$\ln4\times(\log_7x^7-\log_7x^4-\log_7x^3+\log_2y^4-\log_2y^3-\log_2y)$

$0$

$\frac{2\log_78}{\log_74}+\frac{1}{\log_43}\times\log_29=$

$7$

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

$\log_411+\log e^2$

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

$1$

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

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

$\frac{1}{\ln4}\cdot\frac{1}{\log_810}=$

$\frac{3}{2}\log e$

$\log_3x^2\log_527-\log_58=\ln e$

$\pm\sqrt[6]{40}$

$\log_23x\times\log_58=\log_5a+\log_52a$

Given a>0 , express X by a

$\sqrt[3]{\frac{2a^2}{27}}$

Find X

$\ln8x\times\log_7e^2=2(\log_78+\log_7x^2-\log_7x)$

For all x>0

Solve for X:

$\ln x+\ln(x+1)-\ln2=3$

$\frac{-1+\sqrt{1+8e^3}}{2}$

$\frac{\log_8x^3}{\log_8x^{1.5}}+\frac{1}{\log_{49}x}\times\log_7x^5=$

$12$

$\log_x16\times\frac{\ln7-\ln x}{\ln4}-\log_x49=$

$-2$

$\frac{\log_47\times\log_{\frac{1}{49}}a}{c\log_4b}=$

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

$\log_49x+\log_4(x+4)-\log_43=\ln2e+\ln\frac{1}{2e}$

Find X

$-2+\frac{\sqrt{39}}{3}$

$\log_5x+\log_5(x+2)+\log_25-\log_22.5=\log_37\times\log_79$

$-1+\sqrt{6}$