# Logarithms

**Question**

Solve the following questions.

- 3
^{x}= 25 - log
_{3}x = 2 - log
_{3}5

**Answer**

- x = 1.3979/0.4771 = 2.929
- 9
- 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**

**The laws of logarithms**

*log*_{a}m + log_{a}n = log_{a}(m * n) = log_{a}mn*log*_{a}m – log_{a}n = log_{a}(m / n)*log*_{a}m^{b}= b*log_{a}m*log*_{a}1 = 0*log*_{a}a = 1*alog*_{a}x = x*log*_{a}x = log_{b}x/log_{b}a

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