Chapter 5: Q.85 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{5} (x) + \log_{3} (x) = 1$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 1.921$

Step by step solution

Given information

we are given an equation $\log_{5} (x) + \log_{3} (x) = 1$

Simplify and solve for x

We get,

$\frac{\ln x}{\ln 5} + \frac{\ln x}{\ln 3} = 1 \ln 3 \times \ln x + \ln 5 \times \ln x = \ln 5 \times \ln 3 (\ln 3 + \ln 5) \times \ln x = \ln 5 \times \ln 3 \ln x = \frac{\ln 5 \times \ln 3}{\ln 3 + \ln 5} x = 1.921$

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{5} (x) + \log_{3} (x) = 1$

Short Answer

Step by step solution

Given information

Simplify and solve for x

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places: log5x+log3x=1

Short Answer

Step by step solution

Given information

Simplify and solve for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Statistics

Logic and Functions

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{5} (x) + \log_{3} (x) = 1$