What are the two solutions to the absolute value equation |2x+3|=7

Mathematics

1 answer:

wel3 years ago

3 0

Step-by-step explanation: We can solve the equation |2x + 3| = 7 by

first splitting things up into two separate equations.

The first equation will look just like the original problem,

minus the absolute value signs and we have 2x + 3 = 7.

The second equation will look just like the first, only the right

side will be changed to a negative and we have 2x + 3 = -7.

Now solve each equation from here.

In our first equation, subtract 3 from both sides to get 2x = 4.

Then divide both sides by 2 and x = 2.

In our second equation, subtract 2 from both sides to get 2x = -10.

Now, divide both sides by 2 and we have x = -5.

So either x = 2 or x = -5.

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What is the solution to the equation below? Round your answer to two decimal places. log5 x=2.1

Natali5045456 [20]

Answer:

D. x=29.37

Step-by-step explanation:

To answer this question you have to understand how log work. Log is the abbreviation of logarithm and it works as an inverse function of exponentiation.

The rules should be like this:

$log_{a} b = c\\a^{c} = b\\$

Variable a in the equation is called base. If it left empty you can assume its base 10. The log in this question using 5 as a base. Variable b will be x and variable c will be 2.1

Now, let's change the variable of the equation using the information from the question.

$log_{a} b = c\\\log_{5} x = 2.1\\5^{2.1} = x\\x= log_5}^{-1}2.1\\x=29.365473577\\x=29.37$