Find X, If : Log9243 = X - Mathematics

Find x, if : log₉243 = x

Sum

Consider the equation
log₉243 = x
⇒ 9^x = 243
⇒ (3²)^x = 3⁵

⇒ 3^2x = 3⁵

⇒ 2x = 5

⇒ x = `5/2`

⇒ x = `2 1/2`

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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 6.3 | Page 103

Express the following in logarithmic form:

`3^-2 = 1/9`

Express the following in exponential form : log_aA = x

Express the following in exponential form : log₁₀1 = 0

Solve for x : log₁₀ x = -2.

Find the logarithm of : 0.001 to the base 10

Find the logarithm of : `1/16` to the base 4

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

If log_am = n, express a^{n - 1} in terms of a and m.

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

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