# Logarithm Problem

1. Jun 28, 2009

### math4life

1. The problem statement, all variables and given/known data
1) Solve the equation using the exponential form of the equation.

Log2(2-5x)=7

2) Rewrite as a single logarithmic expression:

3log x +(1/2)log z

2. Relevant equations

3. The attempt at a solution

1) I have no idea how to solve this.

2) I know that two logarithms multiply to add, but these have different bases so I do not know what to do.

Thanks.

Last edited: Jun 28, 2009
2. Jun 28, 2009

### rock.freak667

Here is a hint.

$$a^b =c \Rightarrow b= log_a c$$

they are in the same base. Logx usually means log10x.

Use the rule

$$rlog_a x = log_a x^2$$

3. Jun 29, 2009

### Mentallic

I'll just fix up rock.freak667's little typo there.

What was meant to be said is: $$r.log_a(x)=log_a(x^r)$$

Coupled with the rule that $$log_a(b)+log_a(c)=log_a(bc)$$

You should have no problem solving the second one

4. Jun 29, 2009

### Staff: Mentor

I think it might be helpful to add that a logarithm can be thought of as the exponent on the base (the number raised to a power) that results in a particular number. So for example, log10100 means the exponent on 10 that results in 100. In other words, this logarithm is the answer to the question 10? = 100. Pretty clearly, the placeholder represented by ? is 2.

Every equation of the form logbx = y can be rewritten as an equivalent exponential equation by = x, and vice versa, with the only restrictions being that b > 0, and b$\neq$ 1, and x > 0.