106k views
5 votes
(Solve the problem & round the final answer to four decimal places.)

(Solve the problem & round the final answer to four decimal places.)-example-1

1 Answer

3 votes

Given: The logarithm below


log_7√(3)

To Determine: The solution of the given

Solution

Using exponent rule below


√(a)=a^{(1)/(2)}

Applying the exponent rule above to the given logarithm


\begin{gathered} log_7√(3) \\ √(3)=3^{(1)/(2)} \\ Therefore \\ log_7√(3)=log_73^{(1)/(2)} \end{gathered}

Using logarithm rule to the given


\begin{gathered} log_ab^x=xlog_ab \\ Therefore \\ log_73^{(1)/(2)}=(1)/(2)log_73 \end{gathered}

Let us apply change of base as shown below


log_73=(log_e3)/(log_e7)
\begin{gathered} Log_e3=ln3=1.09861 \\ log_e7=ln7=1.94591 \\ log_73=(log_e3)/(log_e7)=(ln3)/(ln7)=(1.09861)/(1.94591)=0.56457 \end{gathered}

Therefore, we have


log_7√(3)=(1)/(2)log_73=(1)/(2)*0.56457=0.28228\approx0.2823(4decimal-place)

Hence, the final answer is approximately 0.2823

User Bluelantern
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories