Question

Solve 4^X = 10^{log₇ (2) + log₇ (2)}

1. log7 (5) + log7 (2)
2. log₇ (8) + log₇ (2)
3. log₇ (5) + log₇ (10)
4. None of the above

Answer 1

Correct Answer - Option 1 : log7 (5) + log7 (2)

Calculation:

4^X = 10^{log₇ (2) + log₇ (2)}

⇒ 4^X = 10^{log₇ (2 × 2)}

Taking log on both sides

⇒ X log (4) = log₇ (4) × log (10)

⇒ X log (4) = log (4) × log (10)/log (7)

⇒ X = log (10)/log (7)

⇒ X = log₇10

⇒ X = log₇ (5) + log₇ (2)

∴ X = log7 (5) + log7 (2)

log₇ (10) = log₇ (5 ×  2)

log (X) + log (Y) = log (X × Y) (True only when bases of log are same)