Prove the following: (log)10 4 ÷ (log) 10 2 = (log)3 9

Given, log 10 4 ÷ log 10 2 = log 3 9 Simplifying L.H.S. we get, ⇒ log 10 4 ÷ log 10 2 = log 10 2 2 ÷ log 10 2 = = 2. Simplifying R.H.S. we get, ⇒ log 3 9 = log 3 3 2 = 2log 3 3 = 2. Since, L.H.S. = R.H.S. Hence, proved that log 10 4 ÷ log 10 2 = log 3 9.

Mathematics

Prove the following:
log₁₀4 ÷ log₁₀2 = log₃9

Logarithms

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Answer

Given,

log₁₀4 ÷ log₁₀2 = log₃9

Simplifying L.H.S. we get,

⇒ log₁₀4 ÷ log₁₀2 = log₁₀2² ÷ log₁₀2

= $\dfrac{2\text{log}$

= 2.

Simplifying R.H.S. we get,

⇒ log₃9 = log₃3²

= 2log₃3

= 2.

Since, L.H.S. = R.H.S.

Hence, proved that log₁₀4 ÷ log₁₀2 = log₃9.

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Mathematics

Prove the following:
log₁₀4 ÷ log₁₀2 = log₃9

Logarithms

Answer

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