Logarithmic Formula Problem


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

1

if expressed by logarithmic notation is

2.gif

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

3.gif

means

4

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



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