Question

Fill in the missing values to make the equations true.(a) log, 11 + logs 9 = logs음8X(b) log ] - log, 7 = log,71(c) log,25

Answer 1

From the rules of doing math using logarithms, we know the following

`\begin{gathered} \text{log A + log B = log (AB)} \\ \text{log A - log B = log (A/B)} \\ \log A^B=B\cdot\log (A) \end{gathered}`

Then, using the data of your question we have the next equation

`\begin{gathered} \log _511+\log _59=\log _5X \\ X=11\cdot9 \\ X=99 \\ \log _511+\log _59=\log _599 \end{gathered}`

The next one will give us the following:

`\begin{gathered} \log _9Y-\log _97=\log _9(8)/(7) \\ (8)/(7)=(Y)/(7) \\ Y=8 \\ \log _98-\log _97=\log _9(8)/(7) \end{gathered}`

The last one will be as follows:

`\begin{gathered} \log _2(1)/(25)=W\cdot\log _25 \\ 5^W=(1)/(25) \\ W=-2 \\ 5^(-2)=(1)/(5^2)=(1)/(25) \\ \log _2(1)/(25)=-2\cdot\log _25 \end{gathered}`