# Homework Help: How do I evaluate this log expression?

1. Jan 4, 2010

### Cuisine123

1. The problem statement, all variables and given/known data
5^(log510-1)
2. Relevant equations
n/a
3. The attempt at a solution
I have no idea how to approach this.

2. Jan 4, 2010

### CompuChip

Well, you know what

$$5^{\log_5(x)}$$
is, don't you?

Then there are two ways to solve the question: you can split the sum in the power to a multiplication:
$$5^{a + b} = 5^a \cdot 5^b$$

or you can first write 1 as a logarithm (base 5), then combine the two logarithms into one.

3. Jan 5, 2010

### Bohrok

Do you know that exponentials and logarithms are inverses of each other?
y = ax $\Longrightarrow$ x = logay
Then, after substituting the x, $$y = a^{\log_a y}$$
So what is $$5^{\log_5 x}$$ ?

Perhaps you should review http://en.wikipedia.org/wiki/Logarithm" [Broken].

Last edited by a moderator: May 4, 2017