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Finger [1]
2 years ago
5

Log10 (2x + 1) - logio(3x - 2) = 1​

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
3 0

Answer: x=3/4

Step-by-step explanation:

To solve, first express the left side as one logarithm. To do so, apply the quotient rule which is log_bM/N=log_bM-log_bN .

log((2x+1)/(3x-2))=1

Then, express the equation to its equivalent exponential form to eliminate the logarithm.

Note that the exponential form of log_b M=a is M=b^a .

Since the base of the logarithm in the given equation is not written, it indicates that its base is 10.

So re-writing the equation, it becomes:

log_10((2x+1)/(3x-2))=1

And its exponential form is:

(2x+1)/(3x-2)=10^1

(2x+1)/(3x-2)=10

Now that the equation has no more logarithm, the next step is to remove the x in the denominator.

To do so, multiply both sides by 3x-2.

(3x-2)*(2x+1)/(3x-2)=10*(3x-2)

2x+1=30x-20

Next, combine like terms.

To combine 30x and 2x, bring them together on one side of the equation. So, move 2x to the right side by subtracting both sides by 2x.

2x-2x+1=30x-2x-20

1=28x-20

To combine 20 and 1, bring them together on the side opposite the term with x. So, add both sides by 20.

1+20=28x-20+20

21=28x

And, divide both sides by 28 to have x only at the right side.

21/28=(28x)/28

3/4=x

Hence, the solution to the given equation is x=3/4 .

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Answer:

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Step-by-step explanation:

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C= \sqrt{80} or 8.94427191...

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I hope this helps!

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3 years ago
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What are the solution(s) for the quadratic equation?<br><br> Y=5x^2-9x+4<br><br> Show work
kakasveta [241]

Let's see

\\ \rm\rightarrowtail 5x^2-9x+4=0

\\ \rm\rightarrowtail 5x^2-5x-4x+4=0

\\ \rm\rightarrowtail 5x(x-1)-4(x-1)=0

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2 years ago
Please help me calculate the value of y with steps
Nutka1998 [239]

The value of y in the triangle is 7.5

<h3>How to calculate the value of y?</h3>

The given parameter is the triangle

On the triangle, we have the following equivalent ratio

y : 8 = y + 15 : 20

Express as fraction

y/8 = y + 15/20

Cross multiply

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Collect the like terms

20y - 8y = 90

Evaluate

12y = 90

Divide by 12

y = 7.5

Hence, the value of y in the triangle is 7.5

Read more about triangles at

brainly.com/question/17335144

#SPJ1

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