147k views
5 votes
Solve each equation some solutions will be expressed using log notation question 6 7 and 8

Solve each equation some solutions will be expressed using log notation question 6 7 and-example-1

1 Answer

4 votes

\begin{gathered} 5)2.498 \\ 6)2.6 \\ 7)3 \\ 8)2 \end{gathered}

5) In this one, let's take the logarithm on both sides:


\begin{gathered} 10^x=315 \\ \log_(10)10^x=\log_(10)315 \\ x=2.498 \end{gathered}

6) Let's begin this exponential equation by simplifying it whenever possible:


\begin{gathered} 2*10^x=800 \\ (2*10^x)/(2)=(800)/(2) \\ 10^x=400 \end{gathered}

Note that we cannot rewrite 400 as a power of base 10, so let's resort to the logarithm:


\begin{gathered} \log_(10)10^x=\log_(10)400 \\ x=2.60 \end{gathered}

Note that according to the property of the logarithm, we can tell that log_10(10)^x is equal to x

7)


\begin{gathered} 10^(\left(1.2x\right))=4000 \\ \log_(10)10^(1.2x)=\log_(10)4000 \\ 1.2x=3.60 \\ (1.2x)/(1.2)=(3.6)/(1.2) \\ x=3.00 \end{gathered}

Note that in this case, we had to take the logarithms on both sides right away.

8)


\begin{gathered} 7*10^(0.5x)=70 \\ (7*10^(0.5x))/(7)=(70)/(7) \\ 10^(0.5x)=10 \\ 0.5x=1 \\ (0.5x)/(0.5)=(1)/(0.5) \\ x=2 \end{gathered}

Note that in this case, after dividing both sides by 7 we ended up with two powers of base 10.

User Indgar
by
9.0k points

No related questions found

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