Evaluate : Log2 ( 1 ÷ 8 )

Evaluate : log₂ ( 1 ÷ 8 )

Sum

Let log₂`1/8` = x

⇒ 2^x = `1/8`
⇒ 2^x = `1/[ 2 xx 2 xx 2 ]`

⇒ 2^x = `1/2^3`

⇒ 2^x = 2^-3⇒ x = - 3
Thus, log₂`1/8` = -3

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Interchanging Logarithmic and Exponential Forms

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Chapter 8: Logarithms - Exercise 8 (A) [Page 103]

Chapter 8 Logarithms
Exercise 8 (A) | Q 7.2 | Page 103

Express the following in logarithmic form:

5³ = 125

Find the logarithm of : 0.1 to the base 10

Find the logarithm of : 0.001 to the base 10

Find the logarithm of : 0.125 to the base 2

State, true or false : If log₁₀ x = a, then 10^x = a.

Find x, if : log₃ x = 0

Find x, if : log₄32 = x - 4

Given log₅y = n. Express 5^{3n + 2} in terms of y.

If log (x² - 21) = 2, show that x = ± 11.

State true or false in the following:
If log ₂ 8 = 3, then log ₈ 2 = `(1)/(3)`