Exercise 38 Page 332

Logarithms can undo a power.

lo g (1 0^{x}) = x

This fact is useful when you have an equation with

x

(or the unknown) in the exponent. However, some equations do not need logarithms, like the one below.

2^{x} = 2^{6}

Since they have the a common base, the exponents are equal, leading to

x = 6 .

But equations with

x

in the exponent and different bases cannot be solved this way. Let's use that information to create an equation.

4^{x} = 7

To solve an equation like this algebraically would require logarithms. Note that this is just one example.