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

Question

asked Aug 20, 2023 59.1k views

1 Answer

John Verco · Answer 1 · 2023-08-25T13:17:42+0000

Given the following exponential equation:

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:

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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:

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