The definition of the logarithm:
The definition of the logarithm:
Where:
is the base of the log
is what appears inside the log - can also appear inside of parentheses
is the exponent to which we raise the base of the log in order to obtain the number that appears inside of the log.
According to the following rule:
In the numerator there will be a log with the base we want to change to, as well as what appears inside of the original log.
In the denominator there will be a log with the base we want to change to, and the content will be the base of the original log.
\( \frac{\log_85}{\log_89}= \)
\( \frac{\log_{4x}9}{\log_{4x}a}= \)
\( \frac{\log_89a}{\log_83a}= \)
\( \frac{\log_9e^2}{\log_9e}= \)
\( \log_74= \)
\( \ln4x= \)
Is inequality true?
\( \log_{\frac{1}{4}}9<\frac{\log_57}{\log_5\frac{1}{4}} \)
\( \frac{2\log_7(x+1)}{\log_7e}=\ln(3x^2+1) \)
\( x=\text{?} \)
\( \frac{\log_4(x^2+8x+1)}{\log_48}=2 \)
\( x=\text{?} \)
Find X
\( \frac{\log_84x+\log_8(x+2)}{\log_83}=3 \)
Is inequality true?
\log_{\frac{1}{4}}9<\frac{\log_57}{\log_5\frac{1}{4}}
Yes, since:
\log_{\frac{1}{4}}9<\log_{\frac{1}{4}}7
Find X
\( \frac{\log_45+\log_42}{3\log_42}= \)
What is the domain of X so that the following is satisfied:
\( \frac{\log_{\frac{1}{8}}2x}{\log_{\frac{1}{8}}4}<\log_4(5x-2) \)
\( \frac{\log_311}{\log_34}+\frac{1}{\ln3}\cdot2\log3= \)
\( \frac{2\log_78}{\log_74}+\frac{1}{\log_43}\times\log_29= \)
\( -3(\frac{\ln4}{\ln5}-\log_57+\frac{1}{\log_65})= \)
What is the domain of X so that the following is satisfied:
\frac{\log_{\frac{1}{8}}2x}{\log_{\frac{1}{8}}4}<\log_4(5x-2)
\frac{2}{3} < x