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:
a log x - b log y = 2 log 3

Solve for x : log₁₀ (x - 10) = 1

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

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

`2/3` log 8

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

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

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b' : log 5.4

State, true or false :
log x x log y = log x + log y

Given that log x = m + n and log y = m - n, express the value of log ` ( 10x ) / ( y ^ 2 )` in terms of m and n.

If log₁₀ 8 = 0.90, find the value of:

log₁₀ 4