This particular topic require deep knowledge of indices, algebra and of course basic understanding of fractions. Above all, all the laws governing indices and logarithms ought to be taken into consideration at all times…that is a MUST.

All the basic laws on indices and logarithms has been posted earlier. Feel free to check it out.

1 = 10º

log₁₀ 1 = 0

10 = 10¹

log₁₀10 = 1

1000 = 10³

log₁₀1000 = 3

27 = 3²

log₃27 = 2

log₁₀10² = 2 log₁₀10 = 2 (1) = 2

Logarithms is another form of mathematics equation. It applies the same principle of addition, subtraction, multiplication and division. It can be factorized or expanded. Today I would like to share with you one or two example of logarithms.

**EXAMPLE 1**

3^x = 15

add log to both side; that will gives you

log 3^x = log 15

x log 3 = log 15

x = log 15/ log 3

Answer could be solved by way of using calculator

**EXAMPLE 2**

Find the value of x when 15^(x – 1) = 3 ^ x

log 15^(x – 1) = log 3^x

(x – 1)log 15 = x log 3

x log 15 – log 15 = x log 3

x log 15 – x log 3 = log 15

x (log 15 – log 3) = log 15

x = log 15/ (log 15 – log 3)

x = log 15/ log (15/3)

x = log 15/ log 5

Answer could be solved by way of using calculator

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