The Sum of Logarithms: Using multiple rules

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

$?=x$

$1$

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

$\log_810$

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

?=x

$112.5$

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

$6$

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

For all 0 < x

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

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

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

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:

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

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

$(2\log_32+\log_3x)\log_23-\log_2x=3x-7$

$x=\text{?}$

$3$

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

Find X

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

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

$-1+\sqrt{6}$

Given 0<a , find X:

$\log_{2a}e^7(\ln a+\ln4a)=\log_4x-\log_4x^2+\log_4\frac{1}{x+1}$

$-\frac{1}{2}+\frac{\sqrt{1+4^{-13}}}{2}$

$\frac{\log_x4+\log_x30.25}{x\log_x11}+x=3$

$x=\text{?}$

$2$

$\log_ax\log_by\log_c2=(\log_ay^3-\log_ay^2)(\log_b\frac{1}{2}+\log_b2^2)\log_c(x^2+1)$

No solution

$\log_59(\log_34x+\log_3(4x+1))=2(\log_54a^3-\log_52a)$

Given a>0 , find X and express by a

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