If Log 10 M = N, Express the Following in Terms of M: 10 N -1

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

Sum

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

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Interchanging Logarithmic and Exponential Forms - Logarithmic to Exponential

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Chapter 10: Logarithms - Exercise 10.1

Chapter 10 Logarithms
Exercise 10.1 | Q 6.1

Express the following in the exponential form:

`"log"_2 (1)/(32)` = -5

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

Express the following in the exponential form:
`"log"_sqrt(3)` 27 = 6

Express the following in the exponential form:

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

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

Find x in the following when: log ₄ 0.0625 = x

Find the value of: log ₃ 81

Find the value of: log _0.1 10

If log ₁₀ x = p, express the following in terms of x: 10^2p-3

If log ₁₀ x = a, log ₁₀ y = b and log ₁₀ z = 2a - 3b, express z in terms of x and y.