Chapter 5: Q.78 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{9} x + 3 \log_{3} x = 14$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 81$

Step by step solution

Given information

We are given an equation $\log_{9} x + 3 \log_{3} x = 14$

Change the base

We get,

$\log_{9} x + 3 \log_{3} x = 14 \frac{\log_{3} (x)}{\log_{3} 9} + 3 \log_{3} x = 14 \frac{\log_{3} (x)}{2} + 3 \log_{3} x = 14 \log_{3} (x) + 6 \log_{3} x = 28 7 \log_{3} x = 28 \log_{3} x = 4$

use the formula y=logax⇔x=ay

We get,

$\log_{3} (x) = 4 x = 3^{4} x = 81$

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{9} x + 3 \log_{3} x = 14$

Short Answer

Step by step solution

Given information

Change the base

use the formula y=logax⇔x=ay

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places: log9x+3log3x=14

Short Answer

Step by step solution

Given information

Change the base

use the formula y=logax⇔x=ay

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Statistics

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{9} x + 3 \log_{3} x = 14$