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Lesson Posted on 01 Jun Indices CBSE/Class 9/Mathematics Schools/ICSE Schools +2 Logarithms CBSE/Class 10 less

Drishti Roy

I have taught primary school students for 2 years. I specialize in Mathematics, Physics and Chemistry...

LOGARITHMIC FUNCTIONS A logarithm is an exponent used in mathematical calculations to depict the perceived levels of variable quantities such as visible light energy, electromagnetic field strength, and sound intensity. Suppose three real numbers a, x, and y are related according to the following equation: x... read more

LOGARITHMIC FUNCTIONS

A logarithm is an exponent used in mathematical calculations to depict the perceived levels of variable quantities such as visible light energy, electromagnetic field strength, and sound intensity.

Suppose three real numbers a, x, and y are related according to the following equation:

x = ay

Then y is defined as the base-a logarithm of x. This is written as follows:

loga x = y

As an example, consider the expression 100 = 102. This is equivalent to saying that the base-10 logarithm of 100 is 2; that is, log10 100 = 2. Note also that 1000 = 103; thus log10 1000 = 3. (With base-10 logarithms, the subscript 10 is often omitted, so we could write log 100 = 2 and log 1000 = 3). When the base-10 logarithm of a quantity increases by 1, the quantity itself increases by a factor of 10. A 10-to-1 change in the size of a quantity, resulting in a logarithmic increase or decrease of 1, is called an order of magnitude. Thus, 1000 is one order of magnitude larger than 100.

Base-10 logarithms, also called common logarithms, are used in electronics and experimental science. In theoretical science and mathematics, another logarithmic base is encountered: the transcendental number e, which is approximately equal to 2.71828. Base-e logarithms, written loge or ln, are also known as natural logarithms. If x = ey, then

loge x = ln x = y

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Arunima G.

Tutor

(-1) power 1/3.
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Solve the equation [(1 / 2) power 2x + 1] = 1?

Math Tutor

-2x-1=0 -2x=1 x=-1/2
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Solve (x) [(y) power m] = y (cube of x) for m?

Math Tutor

log x^2ybase y
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Given: log(5) = b. Express [log base 4(10)] in terms of b?

Narayan Bhat

Math Mentor

(b+log2)/2log2.
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Solve for x the equation: log [log (2 + log (x + 1))] = 0?

Arunima G.

Tutor

(10 power 8) - 1.
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Solve for x the equation: 2 * [(b)power 4 log base b x] = 486?

Narayan Bhat

Math Mentor

3^5/4
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If [log base x (1 / 8)] = -3 / 4, than what is x?

Sarvajeet Kumar

An Experienced Trainer

16
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Solve: log (a / b) + log (b / a) = log (a + b)?

Sarvajeet Kumar

An Experienced Trainer

a+b=1.
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What is the value of log [base 10 (1 / 70)] if log [base 10 (7)] = a?

Chandan Singh

Tutor

log =log =-log =-+log ] = -.
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