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2 years ago

Find the length of side x in simplest radical form with a rational denominator

Mathematics

1 answer:

torisob [31]2 years ago

5 0

Answer:

rggsktvvg gggggggggggg yyyhhhhg

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What are the potential solutions of log4x+log4(x+6)=2?

lions [1.4K]

The potential solutions of $log_4x+log_4(x+6)=2$ are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

Product Rule for Logarithms - $log_{b}(a*c)=log_{b}a+log_{b}c$
Quotient Rule for Logarithms - $log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c$
Power Rule for Logarithms - $log_{b}(a^c)=c*log_{b}a$

The exercise asks the potential solutions for $log_4x+log_4(x+6)=2$ . In this expression you can apply the Product Rule for Logarithms.

$log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0$

Now you should solve the quadratic equation.

Δ= $b^2-4ac=36-4*1*(-16)=36+64=100$ . Thus, x will be $x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}$ . Then:

$x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8$

The potential solutions are 2 and -8.

Read more about the properties of logarithms here:

brainly.com/question/14868849

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1 year ago

A street sign is 8ft 1 inch tall. How tall is it in inches?

xxTIMURxx [149]

Answer:

Step-by-step explanation:

8*12=96+1=97

There are 12 inches for every foot.

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2 years ago

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The price for red paper = 1.25
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Shya works part-time at a gift-wrapping. The store sells wrapping paper rolls and package of wrapping rolls. There are a total o

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The way you wrote the question was a bit confusing. Also, there are two variables here. To find the one variable (the number of rolls of wrapping paper) we need to find the number of packages.

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