## Related questions with answers

Question

Write the following expressions in terms of base e: $\text {(a) } \log _{2}\left(x^{2}-1\right) \text { (b) } \log _{3}(5 x+1) \text { (c) } \log (x+2) \text { (d) } \log _{2}\left(2 x^{2}-1\right)$

Solution

VerifiedStep 1

1 of 3#### (a)

Show the given expression in terms of base $e$.

$\begin{gather*} \log_{2}(x^{2} - 1) = \boldsymbol{\dfrac{\ln(x^{2} - 1)}{\ln(2)}} \end{gather*}$

#### (b)

Show the given expression in terms of base $e$.

$\begin{gather*} \log_{3}(5x + 1) = \boldsymbol{\dfrac{\ln(5x + 1)}{\ln(3)}} \end{gather*}$

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