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

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 the following in a form free from logarithm:

2 log x - log y = 1

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

Evaluate the following without using tables :
log 5 + log 8 - 2 log 2

Prove that : `2"log" 15/18 - "log"25/162 + "log"4/9 = log 2 `

Find x, if : x - log 48 + 3 log 2 = `1/3`log 125 - log 3.

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

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

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 25

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log `2 1/4`

State, true or false :
If `log 25/log 5 = log x`, then x = 2.