Given Log2 X = M. Express 2m - 3 in Terms of X. - Mathematics

Given log₂x = m. Express 2^{m - 3} in terms of x.

Sum

log₂x = m

⇒ 2^m = x
Consider 2^m = x

⇒ `2^m/2^3=x/2^3`

⇒ `2^(m-3)= x/8`

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Interchanging Logarithmic and Exponential Forms

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Chapter 8: Logarithms - Exercise 8 (A) [Page 104]

Chapter 8 Logarithms
Exercise 8 (A) | Q 9.1 | Page 104

Express the following in logarithmic form:

5³ = 125

Express the following in logarithmic form:
10^–3 = 0.001

Express the following in logarithmic form : `(81)^(3/4) = 27`

Express the following in exponential form :
log₁₀0.01 = - 2

Express the following in exponential form : log₁₀1 = 0

Find the logarithm of : 0.001 to the base 10

Find the logarithm of : 27 to the base 9

Find the logarithm of : `1/81` to the base 27

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

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