Logarithmic Function important Formula
- loge𝑥 = log 𝑥 = ln 𝑥
- loga𝑎 = 1
- loga 1 = 0
- loga(𝑥𝑦) = loga𝑥 + loga𝑦
- loga𝑥p= 𝑝 loga 𝑥
- loga(𝑥/𝑦)= loga 𝑥 − loga𝑦
- loga𝑥 = loga 𝑏 . logb𝑥
- 𝑎logam = 𝑚
- 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