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lara [203]
3 years ago
13

PLEASE HELPP ♥

Mathematics
1 answer:
kirza4 [7]3 years ago
4 0

Answer:

An exponential function is a function of the form

f(x)=bx

where b≠1 is a positive real number. The domain of an exponential function is (−∞,∞) and the range is (0,∞).

Solve the equation: 52x−3=752x−3=7.

Since we can’t easily rewrite both sides as exponentials with the same base, we’ll use logarithms instead. Above we said that logb(x)=ylogb⁡(x)=y means that by=xby=x. That statement means that each exponential equation has an equivalent logarithmic form and vice-versa. We’ll convert to a logarithmic equation and solve from there.

52x−3log

⎛⎝⎜

⎞⎠⎟=7=2x−352x−3=7log5

⁡(7

)=2x−3

From here, we can solve for xx directly.

2xx=log5(7)+3=log5(7)+32

A logarithmic function is a function defined as follows

logb(x)=ymeans thatby=xlogb⁡(x)=ymeans thatby=x

where b≠1b≠1 is a positive real number. The domain of a logarithmic function is (0,∞)(0,∞) and the range is (−∞,∞)(−∞,∞).

Solve the equation:

log3(2x+1)=1−log3(x+2).log3⁡(2x+1)=1−log3⁡(x+2).

With more than one logarithm, we’ll typically try to use the properties of logarithms to combine them into a single term.

log3(2x+1)log3(2x+1)+log3(x+2)log3((2x+1)(x+2))log3(2x2+5x+2)2x2+5x+22x2+5x−1=1−log3(x+2)=1=1=1=3=0log3⁡(2x+1)=1−log3⁡(x+2)log3⁡(2x+1)+log3⁡(x+2)=1log3⁡((2x+1)(x+2))=1log3⁡(2x2+5x+2)=12x2+5x+2=32x2+5x−1=0

Let’s use quadratic formula to solve this.

x=−5±52−4⋅2⋅−1−−−−−−−−−−−√2⋅2=−5±

−−−−−−−−⎷4.x=−5±52−4⋅2⋅−12⋅2=−5±33

4.

What happens if we try to plug x=

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Solve the problem algebraically. Clearly define all variables, write an appropriate equation, and solve.
hichkok12 [17]

Answer:

Y=8 and X=21

Step-by-step explanation:

The key to solving word (story) problems is to learn how to translate words and phrases into concise, precise math expressions (variables and operations).  Make a table and add to it as you do problems:

      is              means           =

    more than                        +

      twice                              2*x

      sum                               +

      of                            usually means multiply

     ...

Assign variables.  Try to assign variables to the values the problem asks you to find.

In this problem, there are two variables.   Let x = one number;   y = other numbers

Translate:

 "One number is 5 more than twice the other number"    means

            x          =    5    +        2     *      y

 "sum of the two numbers is 29"     means

      x   +   y                    = 29

Now, the easy math.

Use the value for x from the first equation and substitute that into the second equation:

    (5 + 2y)      +     y       =  29

     5 + 3y = 29                    (collect terms)

           3y = 24                (subtract 5 from both sides)

             y = 8

Now, put that value of y into either equation to solve for x  (Which equation is easier??)

     x + 8 = 29

       x  = 21                 (subtract 8 from both sides)

Checking (very important):

 Is 21 really 5 more than 2(8)?

      21 = 5+16     ?

      21  =  21? yes

 Is  21 + 8 = 29  ?

        29 = 29? yes

p.s., learn the process, don't just get the right answer;  there will be lots of problems that are solved the same way!

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