/*! 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 4 Solve each exponential equation ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 4

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{x}=625$$

Short Answer

Expert verified
The value of x that solves the equation is \(x=4\).

Step by step solution

01

Identify the base

Observe the numbers 5 and 625: both are powers of 5. We can express 5 as \(5^{1}\) and 625 as \(5^{4}\). Thus, we can rewrite the equation \(5^{x}=625\) as \(5^{x}=5^{4}\). This is possible because the base '5' is common to both sides.
02

Equate the exponents

Since the bases are equal (5 in this case), the exponents must be equal as well. Therefore, we equate the exponents: \(x=4\).
03

Confirm the solution

Let's confirm the solution by substituting \(x=4\) into the original equation. \(5^{x}=5^{4}\) simplifies to \(5^{4}=625\), which is the original equation. Thus, the solution is correct.

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

Evaluate each expression without using a calculator. $$\log _{2}\left(\log _{3} 81\right)$$

The function \(W(t)=2600\left(1-0.51 e^{-0.075 t}\right)^{3}\) models the weight, \(W(t),\) in kilograms, of a female African elephant at age \(t\) years. (1 kilogram \(\approx 2.2\) pounds) Use a graphing utility to graph the function. Then \([\text { TRACE }]\) along the curve to estimate the age of an adult female elephant weighing 1800 kilograms.

I can solve \(4^{x}=15\) by writing the equation in logarithmic form.

The formula \(A=36.1 e^{0.0126 t}\) models the population of California, \(A,\) in millions, \(t\) years after 2005 a. What was the population of California in \(2005 ?\) b. When will the population of California reach 40 million?

Write as a single term that does not contain a logarithm: $$e^{\ln 8 x^{5}-\ln 2 x^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.