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mihalych1998 [28]
3 years ago
15

Use the properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic

expressions without using a calculator.​

Mathematics
1 answer:
seraphim [82]3 years ago
6 0

Answer:

xvdsltoqk73jyeu54344y5eg62iuyeytmemymduememwu

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Anja simplified the expression StartFraction 10 x Superscript negative 5 Baseline Over Negative 5 x Superscript 10 Baseline EndF
Gwar [14]

The mistake that Anja made during the simplification of the considered expression is given by: Option C:  She subtracted the coefficients instead of dividing them

<h3>What are coefficients?</h3>

Constants who are in multiplication with variables are called coefficients of those variables.

For example, in 10x^2 we have 10 as coefficient of x^2

Those variables who have got no visible coefficient has 1 as their coefficient. Thus, x^2 has got its coefficient as 1. It is true since 1 multiplied with any number is that number itself.( x^2 = 1 \times x^2 )

<h3>What are some basic properties of exponentiation?</h3>

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c

For the considered situation, the expression that Anja is simplifying is:
\dfrac{10x^{-5}}{-5x^{10}}

Anja simplified it to \dfrac{15}{x^{15}}

She performed operations with variable 'x' correctly since

\dfrac{x^{-5}}{x^{10}} = \dfrac{1}{x^5} \times \dfrac{1}{x^{10}} = \dfrac{1}{x^{15}}

But coefficients will also get divided. Instead of dividing 10 by -5, she subtracted them (as 10 - (-5) = 10 + 5 = 15)

This was her mistake.

The correct simplification would be: \dfrac{10x^{-5}}{-5x^{10}} = \dfrac{10}{-5} \times \dfrac{x^{-5}}{x^{10}} = -2 \times \dfrac{1}{x^{15}} = \dfrac{-2}{x^{15}} = -2x^{-15}

Thus, the mistake that Anja made during the simplification of the considered expression is given by: Option C:  She subtracted the coefficients instead of dividing them

Learn more about exponent and bases here:

brainly.com/question/847241

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2 years ago
Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.
Svetlanka [38]
Step 1 A is correct.....
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Solve for x in the triangle. Round your answer to the nearest tenth
Ilya [14]
Use tan because you are dealing with the opposite and adjacent sides

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What are the slope and the y-intercept of the linear function that is represented by the graph? The slope is 2/3. and the y-inte
olga_2 [115]

Answer:

The equation of a line with a slope of m and a y-intercept of (0, b) is y = mx + b. To graph a line that is written in slope-intercept form: Plot the y-intercept on the coordinate plane. Use the slope to find another point on the line.

Step-by-step explanation:

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Write the slope-intercept form of the equation of each line given the slope and y-intercept.
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Answer:

all work is shown and pictured

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