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Oksanka [162]
3 years ago
14

Solve each exponential equation by using properties of common logarithms. When necessary, round answers to the nearest hundredth

. 7 ^3x-1 = 5 ^x-1
x ≈ 12.33
x ≈ -3.09
x ≈ 0.08
plss help mee
Mathematics
1 answer:
lisabon 2012 [21]3 years ago
7 0

Answer:

0.08

Step-by-step explanation:

Please use parentheses to indicate which operations must be done first.  I 'm choosing to believe that you meant 7^(3x-1) and 5^(x-1).

Taking the common log of both sides, we get:

(3x-1)log 7 = (x-1)log 5

Then 3x·log 7 - log 7 = x log 5 - log 5

Grouping the x terms:

x(3·log 7 - log 5) = log 7 - log 5.  We combine log 7 and log 5, obtaining log (7/5).

Then x(3·log 7 - log 5) = log (7/5).

Solving for x:

      log (7/5)

x = ---------------------

      3·log 7 - log 5

        0.1461

x   = ------------- = 0.08

         1.0363

This agrees with the 3rd answer choice.

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The length of a radius of a circle, measured in centimeters, is represented by the expression x + 1.5. The diameter of the circl
Tomtit [17]

The value of x of a circle with radius x + 1.5 and diameter of 9 2 / 5 cm is 7.9 cm

<h3>Radius of a circle</h3>

Radius of a circle is half of the diameter of a circle. The radius extend from the centre of the circle to the circumference.

Mathematically,

radius = 1 / 2 (diameter)

Therefore,

radius = (x + 1.5) cm

diameter = 9 2 / 5 cm = 47 / 5 cm

let's find x with the relationship above.

Therefore,

x + 1.5 = 47 / 5

subtract 1.5 from both sides

x + 1.5 - 1.5 = 9.4 - 1.5

x = 7.9 cm

learn more on radius here: brainly.com/question/12183018

6 0
2 years ago
Joshua has $560. He wants to buy a laptop that costs $320 as well as a case for the laptop that costs $65 and is currently on sa
Igoryamba

Answer:$154.73

Step-by-step explanation:

Take 65 and multiple .15 and that will give you the 15% off of the case. When u do that you get 9.75 so then 65-9.75= 55.25 multiply .08 for the sales tax on the case = 4.42 add to 55.25= 59.67 then add the sales tax for the laptop 320 multiplied by .08 = 25. 60 for a total of 345.60 then add that to 59.67 = 405.27 then u have to subtract that from 560 and Josh has $154.73

6 0
3 years ago
A man tries to predict the winner of each of twenty football games. Excluding ties, how many different predictions are possible?
ch4aika [34]

Answer:

C) 2(20)

Step-by-step explanation:

In a football game there are 2 teams playing against each other so there are 2 possible winners in a game as either of the 2 teams can win the game. So there are 2 ways to make prediction of winner for a game.

Since, there are 20 football games in total, and predictions of winner per each game are 2, so the possible predictions for 20 games would be 2 x 20

Hence, 2(20)=40 different predictions would be possible for 20 football games.

4 0
3 years ago
Read 2 more answers
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Gnesinka [82]

Answer:

a = 8.1

Step-by-step explanation:

Firstly, since we have a triangle, automatically, we have 3 interior angles

Mathematically the sum of these angles = 180

A + B + C = 180

27 + 25 + C = 180

52 + C = 180

C = 180-52

C = 128

We use the sine rule to find a

The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle

Thus, mathematically according to the sine rule;

c/Sin C = a/Sin A

14/sin 128 = a/sin 27

a = 14sin27/sin 128 = 8.0657

which to the nearest tenth is 8.1

3 0
3 years ago
hiroto solved the equation 6 – 4|2x – 8| = –10 for one solution. his work is shown below. 6 – 4|2x – 8| = –10 –4|2x – 8| = –16 |
fenix001 [56]

Answer:

 x=2 is the other solution.

Step-by-step explanation:

We have been given the equation:  6-4|2x-8|= -10

we will do it by collecting the like terms so the equation will become by shifting 6 on right hand side

-4|2x-8|= -10-6

After simplifying it in first step

-4|2x-8|= -16

We will define the modulus function which is:

|x|=x or -x

So we will consider the negative case

-4(-)(2x-8)=-16

8x-32= -16

8x= -16+32

8x=16

x=2 is the other solution

5 0
3 years ago
Read 2 more answers
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