contestada

Select the correct answer.
Which logarithmic equation is equivalent to this exponential equation?
2,400 = 7,500(10) *
A.
B.
I = log
log (3)
I = -log ()
I = -log (*)
I = log (1)
OC.
D.

Select the correct answer Which logarithmic equation is equivalent to this exponential equation 2400 750010 A B I log log 3 I log I log I log 1 OC D class=

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Answer:

B.

Step-by-step explanation:

2,400 = 7,500[tex](10)^{x}[/tex]

First of all, you want to isolate the [tex](10)^{x}[/tex] by dividing each side by 7,500.

After doing this, you will get

[tex]\frac{2400}{7500}[/tex] = [tex](10)^{-x}[/tex].

Putting this in the logarithmic form, you get [tex]log_{10}[/tex] [tex]\frac{2400}{7500}[/tex] = - x

To get rid of the negative sign, you would simply multiply both dies of the equation by -1. So you would get  [tex]-log_{10} \frac{2400}{7500}[/tex] = x.

When you simplify 2400/7500, you get 8/25, so the answer is B.

Hope this helps!

You can use the definition of logarithm here.

The logarithmic equation that is equivalent to the given exponential function is given by:

Option C:   [tex]x = -\rm log(\dfrac{8}{25})[/tex]

Given logarithmic equation is:

  • [tex]2400 = 7500(10)^{-x}[/tex]

To find:

The equivalent exponential function to given logarithmic equation.

What is the definition of logarithm?

Logarithm is  inverse function to exponentiation.

That means:

[tex]e^a = b \implies a = log_e(b)[/tex]

Transforming given  equation to exponential form:

[tex]2400 = 7500(10)^{-x}\\\\ \dfrac{2400}{7500} = 10^{-x}\\\\ 10^{-x} = \dfrac{8}{25}\\\\ -x = log_{10}(\dfrac{8}{25})\\\\ x = -log_{10}(\dfrac{8}{25})\\\\[/tex]

Since log with base 10 is simply written log, thus,

The logarithmic equation that is equivalent to the given exponential function is given by:

Option C:   [tex]x = -\rm log(\dfrac{8}{25})[/tex]

Learn more about logarithm here:

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