Solve each equation. Show all your work. Round your answers to four decimal places.
17.) log7 (x +1) + log7(x – 5) = 1

Question

Solve each equation. Show all your work. Round your answers to four decimal places.  
17.) log7 (x +1) + log7(x – 5) = 1

mathstudent55 · Answer

This is a rule of logs:

$ \log a + \log b = \log (ab) $

mertsj · Answer

$$\log_{7}(x-1)+\log_{7}(x+5)=1  $$
$$\log_{7}(x-1)(x+5)=1 $$

mertsj · Answer

Now put that equation into its exponential form.

mathstudent55 · Answer

That means change the form of the equation form the left to the right as shown below.
$ log_b x = y \iff b^y = x$

anonymous · Answer

so x^2 - 5 = 1 
    x^2 = -4?

mertsj · Answer

What is the base?

anonymous · Answer

log7?

mertsj · Answer

The base is 7.  What is the exponent?

anonymous · Answer

how would i find that?

mertsj · Answer

The log is the exponent.  You equation says:  log (       )=1
That means the exponent is 1

mertsj · Answer

So you know the base and you know the exponent

mertsj · Answer

Write that.  It is equal to the expression in the parentheses

anonymous · Answer

4?

mertsj · Answer

What is the base?

mathstudent55 · Answer

Here's an example of how to convert from log form to exponential form.
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