If Log 10 M = N, Express the Following in Terms of M: 10 -3n - Mathematics

If log ₁₀ m = n, express the following in terms of m: 10 ^-3n

Sum

10 ^-3n
log ₁₀ m = n
⇒ m = 10 ⁿ
∴ 10 ^-3n
= (10 ⁿ)^-3
⁼ (m)^-3
= `(1)/("m"^3)`.

shaalaa.com

Interchanging Logarithmic and Exponential Forms - Logarithmic to Exponential

Is there an error in this question or solution?

Chapter 10: Logarithms - Exercise 10.1

Chapter 10 Logarithms
Exercise 10.1 | Q 6.3

Express the following in the exponential form:
log₅ a = 3

Express the following in the exponential form:

`"log"_25 sqrt(5) = (1)/(4)`

Express the following in the exponential form:
q = log_a p

Find x in the following when: log _x 243 = 5

Find x in the following when: log ₈ x = `(2)/(3)`

Find the value of: log ₅ 125

Find the value of: log _0.1 10

If log ₁₀ m = n, express the following in terms of m: 10^{n -1}

If log ₁₀ x = p, express the following in terms of x: 10^2-p

If Iog ₁₀a = x, log₁₀ b = y and log ₁₀ c = z, find
10^2x-3in term of a