Find the Value Of: Log √ 3 ( 3 √ 3 )

Find the value of: `"log_sqrt(3) (3sqrt(3))`

Sum

`"log_sqrt(3) (3sqrt(3))`

Let `"log_sqrt(3) (3sqrt(3))` = x

⇒ `(sqrt(3))^x = 3sqrt(3)`

⇒ `3^(x/2) = 3^(1 + 1/2) = 3^(3/2)`

∴ `x/(2) = (3)/(2)`
⇒ x = 3.

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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 4.16

Express the following in the exponential form:
log₁₀ 0.001 = -3

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

Express the following in the exponential form:
-2 = log₂ 0.25

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

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

Find the value of: log ₃ 81

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

If log ₁₀ x = a, express the following in terms of x: 10 ^{a + 3}

If log ₁₀ m = n, express the following in terms of m: 10 ²ⁿ⁺¹

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