Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 7 (page 351)

Solve each equation
$\log_{5} x = 4$

Short Answer

Expert verified

The value of x is 625.

Step by step solution

Step 1. Given Information

Given equation $\log_{5} x = 4$

We have to solve equation for the value of x.

Step 2. Solution

Logarithmic function is good defined only if the argument of logarithmic function is a positive real number $(\log_{b} x, x > 0)$ .

Therefore, the solutions of equation $\log_{5} x = 4$ must be $x > 0 - - - (1)$

Using the formula

role="math" localid="1646582146253" $y = \log_{a} x 鈬� x = a^{y} a > 0, a 鈮� 1 (w h e r e a = 5 a n d y = 4) w e g e t \log_{5} x = 4 x = 5^{4} x = 625$

The solution is greater than 0 (because of (1)) , so the solution of the given equation is x = 625

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91影视

Solve each equation
$\log_{5} x = 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

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91影视

Solve each equationlog5x=4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Geometry

Decision Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each equation
$\log_{5} x = 4$