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Iteru [2.4K]
3 years ago
9

How do you evaluate logarithms? Explain using an example or mathematical evidence to support your answer.

Mathematics
2 answers:
kenny6666 [7]3 years ago
6 0

Answer: Explanation below.

Step-by-step explanation:

First of all you need to know how to convert a logarithm into an exponential expression. The property is:

log_Bx=n

This is the same as: B^n=x

Example 1:

log_99=

We are trying to find what to raise 9 to, in order to get a result of 9.

9^x=9

When you have same bases, you equal exponents.

x=1

Therefore; log_99=1

Example 2:

log_232=

2^x=32

In this case, we have to make sure both sides have the same base. 32 can have a base of 2 if expressed as: 2^5 which is 2*2*2*2*2

Rewriting this example we have;

2^x=2^5

Since we have the same base, we equal exponents.

x=5

Therefore; log_232=5

Example 3:

log_3729=

3^x=729

729 can have a base of 3 if expressed as: 3^6

3^x=3^6

x=6

zvonat [6]3 years ago
4 0

Answer:

  use a calculator

Step-by-step explanation:

The logarithm function is a transcendental function not generally amenable to calculation by hand (possibly except when logarithms are small integers). It can only be evaluated for numbers. The logs of variable expressions can only be indicated.

Attached is an example of a calculator giving the natural log of 2.

_____

<em>Comment on hand calculation</em>

Before the advent of computers, logarithms were calculated by hand. It often took many years of calculation to produce usable tables of logarithms. Not only were logs of numbers provided in tables, but also logs of trig functions of angles. The latter greatly aided global navigation, making it possible to easily compute navigation functions.

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solong [7]

Answer:

4 √6

Step-by-step explanation:

We have a few right triangles. We know that a²+b²=c², with c being the side opposite the right angle. Representing the side without a value as z, we have:

m²+z² = (8+4)² = 12²

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We have 3 equations with 3 unknown variables, so this should be solvable. One way to find a solution is to put everything in terms of m and go from there. First, we can take n out of the equations entirely, removing one variable. We can do this by solving for it in terms of z and plugging that into the third equation, removing a variable as well as an equation.

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plug that into the third equation

64 + z² - 16 = m²

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z² = m² - 48

plug that into the first equation

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192 = 2m²

divide both sides by 2 to isolate the m²

96 = m²

square root both sides to solve for m

√96 = m

we know that 96 = 16 * 6, and 16 = 4², so

m = √96 = √(4²*6) = 4 √6

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Answer:

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Hope this helps ^-^

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