Given the following exponential equation:
[tex]11^x=189[/tex]
a) give solution in calculator ready form the exact value of x.
So, taking ln for both sides
[tex]\begin{gathered} \ln 11^x=189 \\ x\ln 11=\ln 189 \end{gathered}[/tex]
so, the form for the exact value of (x) will be as follows:
[tex]x=\frac{\ln 189}{\ln 11}[/tex]
b) approximate the solution to the nearest hundredth
By the calculator the answer will be as follows:
[tex]x=2.19[/tex]
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The logarithm form of the given exponential equation will be as follows:
[tex]x=\log _{11}189[/tex]
Using the following rule of the logarithm:
[tex]\begin{gathered} \log _ab=\frac{\log b}{\log a} \\ \\ x=\log _{11}189=\frac{\log 189}{\log 11} \end{gathered}[/tex]
