Exponential & Logarithmic Equations

**paigesisco** · March 22nd 2013, 10:04 AM

log base (2) (x) +long base(2) (3) = log base(2) (18)

**Plato** · March 22nd 2013, 10:59 AM

Originally Posted by paigesisco

log base (2) (x) +long base(2) (3) = log base(2) (18)

What can you do with $\log_2(x)=\log_2(18)-\log_2(3)~?$

**cogito** · March 22nd 2013, 11:11 AM

You can use the rules for calculating with logarithms. In general

$\log_a x + \log_a y = \log_a (xy)$

and

$\log_a x - \log_a y = \log_a \left(\frac{x}{y}\right)$ .

For your problem

$\log_2 x - \log_2 18 + \log_2 3 = 0$

transforms to

$\log_2\left(\frac{3x}{18}\right) = 0$

or

$\frac{3x}{18} = 1$

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