Logarithms

When learning logarithm function in secondary mathematics classes, students are likely to introduced with the law of logarithms and also their corresponding graph. In addition to that, they are also likely to deal with situation whereby they need to solve logarithmic functions. Sometime knowing on how to change the base of logarithms can be useful when solving the function.

Question

Solve the following questions.

1. 3^x = 25
2. log₃x = 2
3. log₃5

Answer

1. x = 1.3979/0.4771 = 2.929
2. 9
3. x = 0.69897/0.4771 = 1.465

Note:

• If you remember the laws of logarithms, you may notice that sometimes logarithms expression can be written in different ways.
• You may see from below on how the logarithm expression can be simplied (eg. when logorithms with same base be added or subtracted from one another).

The laws of logarithms

• log_am + log_an = log_a(m * n) = log_amn
• log_am – log_an = log_a(m / n)
• log_am^b = b*log_am
• log_a1 = 0
• log_aa = 1
• alog_ax = x
• log_ax = log_bx/log_ba

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