Gupta Tutorial

Logarithmic Function

Logarithmic Function important Formula

  1. loge𝑥 = log 𝑥 = ln 𝑥
  2. loga𝑎 = 1
  3. loga 1 = 0
  4. loga(𝑥𝑦) = loga𝑥 + loga𝑦
  5. loga𝑥p= 𝑝 loga 𝑥
  6. loga(𝑥/𝑦)= loga 𝑥 − loga𝑦
  7. loga𝑥 = loga 𝑏 . logb𝑥
  8. 𝑎logam = 𝑚
  9. logx𝑦 =log 𝑦 /l og x

Examples: 1. If the graph of 𝑦 = 𝑎x contains the points (3,64) then the base a is (2077 Questions)

a. 4 b. 3 c. 64 d. 2

Solution: Given,
𝑦 = 𝑎x ———(i) and point is (3,64)
Putting the given point in equation(i) we get,
64 = a3
Or, 43=a3
Hence, the base is same so a=4
Hence, the correct answer is option a. 4

Example: 2. If log2(𝑥 − 7) = 1 then x is (2074 Questions)

a. Not Known b. 8 c. 6 d. 9

Solution: Given,
log2(𝑥 − 7) = 1———–(i)
Put the value of x from the given option.
We know that,

loga𝑎 = 1

So,
From option d.log2(9 − 7)

log2(2) = 1 ( From loga𝑎 = 1 )

Hence, the correct answer is option d. 9

Some important Formula of Hyperbolic Function

For Video Check it out

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