/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 106 Evaluate each expression without... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 106

Evaluate each expression without using a calculator. $$\log _{5}\left(\log _{2} 32\right)$$

Short Answer

Expert verified
The value of the expression \(\log _{5}\left(\log _{2} 32\right)\) is 1.

Step by step solution

01

Evaluate The Inner Logarithm

Begin by evaluating the inner logarithm \(\log_2 32\). Given that \(2^5 = 32\), it follows that \(\log_2 32 = 5\). So the expression simplifies to \(\log_5 5\).
02

Evaluate The Outer Logarithm

The next step is to evaluate \(\log_5 5\). Given that \(5^1 = 5\), it is clear that \(\log_5 5 = 1\). Therefore, the expression simplifies to 1.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

In Exercises \(53-56,\) rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$ y=2.5(0.7)^{x} $$

Find the domain of each logarithmic function. $$f(x)=\log \left(\frac{x-2}{x+5}\right)$$

Without using a calculator, find the exact value of $$\frac{\log _{3} 81-\log _{\pi} 1}{\log _{2 \sqrt{2}} 8-\log 0.001}$$

Find the domain of each logarithmic function. $$f(x)=\log \left(\frac{x+1}{x-5}\right)$$

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$3^{x}=2 x+3$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.