Exercise 9 Page 323

Let's consider how logarithms work. When taking the logarithm of something, we can undo exponents.

lo g a^{m} = m lo g a

This is why it does not make any sense solving equations such as

56 = x^{8}

with logarithms.

lo g x^{8} = 8 lo g x

As we can see,

x

is in the argument of the logarithms which means it is not solved for. However, when the equation is

2 = 1.0 4^{x},

we can use logarithms to isolate

x .

lo g 1.0 4^{x} = x lo g 1.04

Here we see that the variable is in the base of the power. This kind of equation we solve using radicals.