Test: Logarithmic Functions - JEE MCQ

Given:
log₂₇x = 1/6

Concept used:
If Log_ex = z, then x = e^z

Calculation:
log₂₇x = 1/6
⇒ x = 27^1/6 = √3
∴The answer is √3.

log₁₀ 2 = 0.3010 and log₁₀ 3 = 0.4717
Now, 
log₁₀ 4.5 = log₁₀ (9/2)
= log₁₀ 9 - log₁₀ 2 (∵ log(m/n) = log m - log n)
= log₁₀ 32 - log₁₀ 2
= 2log₁₀ 3 - log₁₀ 2
= 2(0.4771) - 0.3010 = 0.6532

Formula used:

Calculation:

By using the above property
⇒ x² - 4x + 5 = x -1
⇒ x² - 5x + 6 = 0
⇒ x² - 2x - 3x + 6 = 0
⇒ x(x - 2) - 3(x - 2) = 0
⇒ (x - 2)(x - 3) = 0
∴ x = 2 & 3

Concept:
Logarithm properties:  

Product rule: The log of a product equals the sum of two logs.
log_a(mn) = log_am + log_an

Quotient rule: The log of a quotient equals the difference of two logs.

Power rule: In the log of power the exponent becomes a coefficient.

Formula of Logarithms:

Calculation: