Question

#6 solve a) give solution in calculator ready form the exact value of x b) approximate the solution to the nearest hundredth

Answer 1

Given the following exponential equation:

`11^x=189`

a) give solution in calculator ready form the exact value of x.

So, taking ln for both sides

`\begin{gathered} \ln 11^x=189 \\ x\ln 11=\ln 189 \end{gathered}`

so, the form for the exact value of (x) will be as follows:

`x=(\ln 189)/(\ln 11)`

b) approximate the solution to the nearest hundredth

By the calculator the answer will be as follows:

`x=2.19`

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The logarithm form of the given exponential equation will be as follows:

`x=\log _(11)189`

Using the following rule of the logarithm:

`\begin{gathered} \log _ab=(\log b)/(\log a) \\ \\ x=\log _(11)189=(\log 189)/(\log 11) \end{gathered}`