Question

Look at the way the following exponential equation was solved for x.

Somewhere in the steps, an error was made.
a. Where was the error made? Pick one:
Going to Step 1 Going to Step 2 Going to Step 3 Going to Step 4 Going to Step 5
Write the specific part of the problem that is wrong here:

b. Explain why it is a mistake and what should be done instead.

C. Work out the rest of the problem correctly, showing your work step by step.



Work out the rest of the problem correctly, showing your work step by step.

Answer 1

Answer/Step-by-step explanation:

a. The mistake was "Going to Step 1".

The specific part of the problem that is wrong is$(5^3)$

b. It is wrong because applying the negative exponent rule (i.e. $\frac{1}{a^x} = a^{-x}$, we should have:

$(5^{-3})$ NOT $(5^3)$, because $(\frac{1}{125}) = (5^{-3})$.

c. Here's how to work out the rest of the problem correctly.

$5^{x - 4} = (\frac{1}{125})^{2x + 1}$

1. $5^{x - 4} = (5^{-3})^{2x + 1}$

2. $5^{x - 4} = 5^{-6x - 3}$ (distributive property)

3. $x - 4 = -6x - 3$ (5 cancels 5)

4. $7x - 4 = - 3$ (addition property of equality)

5. $7x = 1$ (addition property of equality)

6. $x = \frac{1}{7}$ (division property of equality)