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Kryger [21]
4 years ago
7

What does multiplication translate to when using logs?

Mathematics
2 answers:
const2013 [10]4 years ago
7 0

General Idea:

We can use the product rule for exponentiation to derive a corresponding product rule for logarithms.

e^a \cdot e^b=e^{a+b}

Also we knowe^{ln(m)}=m

Using the above rule we can write the below equation...

e^{ln(xy)}=xy \; \rightarrow 1^{st} \; equation\\ \\ e^{ln(x)}=x \; \rightarrow \; 2^{nd} \; equation\\ \\ e^{ln(y)}=y \; \rightarrow \; 3^{rd} \; equation\\ \\ Substituting \; 2^{st} \;  equation \; and \; 3^{rd} \; equation\; in\; 1^{st}\; equation, \; we\; get...\\ \\ e^{ln(xy)}=e^{ln(x)} \cdot e^{ln(y)}\\ \\ Applying \; the \; formula\; of\; exponent\; in\; right\; sides\; of\; equation\\ \\ e^{ln(xy)}=e^{ln(x)+ln(y)}\\ \\ Taking \; natural \; logarithm\; on\; both\; sides\\ \\

ln[e^{ln(xy)}]=ln[e^{ln(x)+ln(y)}]\\ \\ And \; using\; the\; formula\; lnm^n=n(lnm), we\; get...\\ \\ ln(xy)=ln(x)+ln(y)

Conclusion:

The product rule for exponentiation

e^{x} \cdot e^{y}=e^{x+y}

The product rule of logarithms

ln(xy)=ln(x)+ln(y)

4vir4ik [10]4 years ago
6 0
It translates to addition.
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Answer:

16 cars.

Step-by-step explanation:

Let x represent number of sold cars.

We have been that 1st company pays a salary of $8000 plus a commission of $900 for each car sold. We can represent this information in an expression as:

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We are also told that second company pays a salary of $14400 plus a commission of $500 for each car sold. We can represent this information in an expression as:

500x+14,400

To find the number of cars sold, which will make the total pay the same, we will equate both expressions and solve for x as:

900x+8000=500x+14,400

900x-500x+8000=500x-500x+14,400

400x+8000-8000=14,400-8000

400x=6,400

\frac{400x}{400}=\frac{6,400}{400}

x=16

Therefore, 16 cars would need to be sold to make the total pay the same.

3 0
4 years ago
Hannah purchased three items at the store for $7.05, $8.12, and $3.97. She paid for
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Answer:

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Step-by-step explanation:

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3 years ago
What is an expression equivalent to x - 3y + 4
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Answer:

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What is the equation of a circle whose center is at the origin and whose radius is 9?
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