Find X, If : Log9243 = X

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:
10^–3 = 0.001

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

Express the following in exponential form : log₁₀1 = 0

Solve for x : log₁₀ x = -2.

Find x, if : log₄32 = x - 4

Find x, if : log₇ (2x² - 1) = 2

Evaluate : log₅ 125

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

Solve for x:

log(x - 1) + log (x + 1) = log₂1

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