Question

Evaluate 5 log10 2+3/2 log10 25 + 1/2 log10 49 - log10, 28 ?
2)3
1) 2
34
11 2
4) 5​

Answer 1

Answer:

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Answer 2

logb(x) = y

x = logb(bx)

logb(x) = y is equivalent to x = by

b: log base number, b>0 and b≠1

x: is real number, x>0

Logarithm

Logarithm is considered to be one of the basic concepts in mathematics. There are plenty of definitions, starting from really complicated and ending up with rather simple ones. In order to answer a question, what a logarithm is, let's take a look at the table below:

21 22 23 24 25 26

2 4 8 16 32 64

This is the table in which we can see the values of two squared, two cubed, and so on. This is an operation in mathematics, known as exponentiation. If we look at the numbers at the bottom line, we can try to find the power value to which 2 must be raised to get this number. For example, to get 16, it is necessary to raise two to the fourth power. And to get a 64, you need to raise two to the sixth power.

Therefore, logarithm is the exponent to which it is necessary to raise a fixed number (which is called the base), to get the number y. In other words, a logarithm can be represented as the following:

logb x = y

with b being the base, x being a real number, and y being an exponent.

For example, 23 = 8 ⇒ log2 8 = 3 (the logarithm of 8 to base 2 is equal to 3, because 23 = 8).

Similarly, log2 64 = 6, because 26 = 64.