Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 8

Express the following statements using logarithms: (a) \(8^{2}=64\) (b) \(4^{3}=64\) (c) \(2^{6}=64\)

Short Answer

Expert verified
Question: Rewrite the given exponential equations in logarithmic form: (a) \(8^{2}=64\) (b) \(4^{3}=64\) (c) \(2^{6}=64\) Answer: (a) \(\log_{8}(64)=2\) (b) \(\log_{4}(64)=3\) (c) \(\log_{2}(64)=6\)

Step by step solution

01

(Step 1: Understand the logarithmic function)

The logarithm function is the inverse of an exponential function. Given an equation \(a^x=b\), we can rewrite it as a logarithm equation using the following format: \(\log_{a}(b)=x\). In this problem, we have three equations to transform from the exponential form to the logarithmic form.
02

(Step 2: Transform equation a)

For the first equation \(8^{2}=64\), we can rewrite it using the logarithm with base 8 as follows: \(\log_{8}(64)=2\).
03

(Step 3: Transform equation b)

For the second equation \(4^{3}=64\), we can rewrite it using the logarithm with base 4 as follows: \(\log_{4}(64)=3\).
04

(Step 4: Transform equation c)

For the third equation \(2^{6}=64\), we can rewrite it using the logarithm with base 2 as follows: \(\log_{2}(64)=6\). In conclusion, the given statements have been expressed in logarithmic form as: (a) \(\log_{8}(64)=2\) (b) \(\log_{4}(64)=3\) (c) \(\log_{2}(64)=6\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write the following using logarithms: (a) \(32=2^{5}\) (b) \(125=5^{3}\) (c) \(243=3^{5}\) (d) \(4^{3}=64\) (e) \(6^{2}=36\)

Solve (a) \(\mathrm{e}^{x}=5\) (b) \(\mathrm{e}^{x}=0.5\) (c) \(\mathrm{e}^{x}=25\) (d) \(\mathrm{e}^{x}=0.001761\)

The current in a circuit, \(i(t)\), is given by $$ i(t)=25 \mathrm{e}^{-0.2 t} \quad t \geq 0 $$ (a) State the current when \(t=0\). (b) Calculate the value of the current when \(t=2\) (c) Calculate the time when the value of the current is \(12.5\).

An amplifier has a gain of \(25 \mathrm{~dB}\). If the input voltage is \(15 \mathrm{mV}\) calculate the output voltage.

Express \(6 e^{x}+3 \mathrm{e}^{-x}\) in terms of the hyperbolic functions \(\sinh x\) and \(\cosh x\).
See all solutions

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Read Explanation

Space Physics

Read Explanation

Particle Model of Matter

Read Explanation

Solid State Physics

Read Explanation

Physics of Motion

Read Explanation

Conservation of Energy and Momentum

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free