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" $y = \log_{a} x \Leftrightarrow x = a^{y} a > 0, a \neq 1 (w h e r e a = 5 a n d y = 4) w e g e t \log_{5} x = 4 x = 5^{4} x = 625$

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

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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

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Logic and Functions

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