Solve for X : Log (X2 - 21) = 2 - Mathematics

Solve for x : log (x² - 21) = 2.

Sum

log ( x² - 21 ) = 2
⇒ log ( x² - 21) = log 100
⇒ x² - 21 - 100 = 0
⇒ x² - 121 = 0
⇒ x² = 121
⇒ x = `+- sqrt121`
⇒ x =`+-`11

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Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (B) [Page 106]

Chapter 8 Logarithms
Exercise 8 (B) | Q 7.2 | Page 106

Express in terms of log 2 and log 3:

log 144

Express in terms of log 2 and log 3 : log 4.5

Express in terms of log 2 and log 3:

`log26/51 - log91/119`

Express in terms of log 2 and log 3 :
`"log"75/16 - 2"log"5/9 + "log"32/243`

Express the following in a form free from logarithm:
a log x - b log y = 2 log 3

Evaluate the following without using tables :
log₁₀8 + log₁₀25 + 2 log₁₀3 - log₁₀18

Solve for x : log₁₀ (x - 10) = 1

Solve for x : log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3

Solve for x :
`log 225/log15` = log x

If log₁₀ 8 = 0.90, find the value of:

log₁₀ 4