**Logarithmic formula**

Well, for those of you who aren’t familiar with logarithms, here we explain about the notion of logarithms in easily understood languages. Basically the notion of logarithms is a mathematical operation that is the inverse of the exponent or lift. Example of the logarithm of the exponent

if expressed by logarithmic notation is

With the following information:

a = base or principal number

b = result or range of logarithms

c = numerus or logarithmic domain.

Note, it is important for you to know before we discuss further about the logarithmic formula that writing

means

**Logarithmic properties**

Here is an example of the logarithmic properties that we will write in the logarithmic table below.

If a> 0, a ≠ 1, m ≠ 1, b> 0 and c> 0, then apply:

In essence, the nature of the formula that we need to memorize is as follows. Some basic formulas or logistical properties that we need to know:

**Examples of Logarithmic Problems**

1). If log 2 = a

then log 5 is …

answer:

log 5 = log (10/2) = log 10 – log 2 = 1 – a (because log 2 = a)

2). √15 + √60 – √27 = …

Answer:

√15 + √60 – √27

= √15 + √ (4 × 15) – √ (9 × 3)

= √15 + 2√15 – 3√3

= 3√15 – 3√3

= 3 (√15 – √3)

3). log 9 per log 27 = …

Answer:

log 9 / log 27

= log 3² / log 3³

= (2. log 3) / (3. log 3) <- remember the nature of log a ^ n = n. log a

= 2/3

4). √5-3 per √5 +3 = …

Answer:

(√5 – 3) / (√5 + 3)

= (√5 – 3) / (√5 + 3) x (√5 – 3) / (√5 – 3) <- times the root of the friend

= (√5 – 3) ² / (5 – 9)

= -1/4 (5-6√5 + 9)

= -1/4 (14 – 6√5)

= -7/2 + 3 / 2√5

= (3√5 – 7) / 2

5). If a log 3 = -0.3 show that a = 1/81 3√9

Answer:

ª log 3 = -0.3

log 3 / log a = -0.3

log a = – (10/3) log 3

log a = log [3 ^ (- 10/3)]

a = 3 ^ (- 10/3) = 3 ^ (- 4) (3²) ^ (⅓)

a = 1/81 3√9

6). log (3a – √2) on a 1/2 base. Determine the value of a!

Answer:

[log (3a – √2)] / log (0.5) = -0.5

log (3a – √2) = -0.5 log 0.5 = log (1 / √½)

3a – √2 = 1 / √½

a = (2/3) √2