/*! 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 54 Solve the following equations. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 54

Solve the following equations. $$2^{x}=55$$

Short Answer

Expert verified
Answer: The approximate value of x is \(5.78\).

Step by step solution

01

Write down the given equation

We are given the following equation to solve: $$2^{x}=55$$
02

Apply natural logarithm on both sides

In order to find the value of x, we will apply the natural logarithm on both sides of the equation. It gives us: $$\ln(2^x) = \ln(55)$$
03

Use logarithmic property

Using the property of logarithms which states that \(\ln(a^b)=b \cdot \ln(a)\), we can rewrite the equation as: $$x \cdot \ln(2)=\ln(55)$$
04

Solve for x

To isolate x and find its value, we simply divide both sides of the equation by \(\ln(2)\): $$x=\frac{\ln(55)}{\ln(2)}$$
05

Evaluate the expression

Evaluating the expression using a calculator: $$x \approx 5.78$$ Thus, the solution for the given equation is \(x \approx 5.78\).

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

Beginning with the graphs of \(y=\sin x\) or \(y=\cos x,\) use shifting and scaling transformations to sketch the graph of the following functions. Use a graphing utility only to check your work. $$g(x)=-2 \cos (x / 3)$$

Design a sine function with the given properties. It has a period of 12 hr with a minimum value of -4 at \(t=0 \mathrm{hr}\) and a maximum value of 4 at \(t=6 \mathrm{hr}\)

Use the definition of absolute value to graph the equation \(|x|-|y|=1 .\) Use a graphing utility only to check your work.

a. Find the linear function \(C=f(F)\) that gives the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that \(C=0\) when \(F=32\) (freezing point) and \(C=100\) when \(F=212\) (boiling point). b. At what temperature are the Celsius and Fahrenheit readings equal?

Simplify the difference quotients \(\frac{f(x+h)-f(x)}{h}\) and \(\frac{f(x)-f(a)}{x-a}\) by rationalizing the numerator. $$f(x)=\sqrt{x^{2}+1}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.