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kotykmax [81]
3 years ago
10

How do I solve for x here? Use the properties of logarithms to find a value for x. Assume a,b, and M are constants.

Mathematics
1 answer:
Leona [35]3 years ago
7 0

Yes, you're right! The first step is rewriting the equation as

\ln(a) + \ln(b^x) = M

Subtract \ln(a) from both sides:

\ln(b^x) = M-\ln(a)

Use the property \ln(a^b) = b\ln(a) to rewrite the equation as

x\ln(b) = M-\ln(a)

Divide both sides by \ln(b)

x = \dfrac{M-\ln(a)}{\ln(b)}

Alternative strategy:

Consider both sides as exponents of e:

e^{\ln(ab^x)} = e^M

Use e^{\ln(x)} = x to write

ab^x = e^M

Divide both sides by a:

b^x = \dfrac{e^M}{a}

Consider the logarithm base b of both sides:

x = \log_b\left(\dfrac{e^M}{a}\right)

The two numbers are the same: you can check it using the rule for changing the base of logarithms

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3 years ago
An electronic system has each of two different types of components in joint operation. Let X and Y denote the lengths of life, i
AURORKA [14]

Answer:

a

The average cost is E(C) = 66

b

The standard deviation of  cost is  \sigma  = 9.798

Step-by-step explanation:

From the question we are told that

          E(X) =  4

          E(Y) =  2

          E(X^2) =  24

           E(Y^2) =  8

The cost of replacing the two component is  C =  50 + 2 X + 4 Y

The variance   of X is mathematically represented as

           V(X) =  E(X^2) - [E(X)]^2

Substituting values  

              V[X] =  24 - 4^2

               V[X] =8

The variance  of Y is mathematically represented as

           V(Y) =  E(Y^2) - [E(Y)]^2

Substituting values  

              V[Y] =  8 - 2^2

               V[X] =4

The average of  replacing the two component is  

        E(C) =  2 * E(X)  + 4* E(Y)

substituting value

         E(C) =  50 + 2 * (4)  + 4* (2)

         E(C) = 66

The variance  of replacing the two component is  

        V(C) = V(50 + 2X +4Y)      Note: The variance of constant is zero

                                                                  and X and  Y are independent  

=>      V(C) =  2^2 * V(X) + 4^2 * V(Y)

substituting values

=>       V(C) =  4 * 8 +  16 * 4        

=>         V(C) =  32 + 64

=>         V(C) = 96

The standard deviation is

         \sigma  =  \sqrt{V(C)}  

substituting values

           \sigma  =  \sqrt{96}

           \sigma  = 9.798

6 0
3 years ago
You back packed for a distance of 15.75 miles today. You back packed at an average speed of 1.26 miles per hour, how long did yo
Anna [14]

Let us first concentrate and write down all the information's given in the question. Based on these information's the answer to the question can be easily deduced.
Distance for which back packing was done = 15.75 miles
Average speed of back packing = 1.26 miles/hour
Since
Speed = Distance/Time
Time = Distance/speed
Time spend for back packing = 15.75/1.26 hour
                                               = 12.5 hour
So the total time taken for back packing is 12.5 hours. I hope this is the answer you were looking for and the procedure is clear to you.
7 0
3 years ago
What is the slope on ​
Tema [17]

Answer:

-3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
How many solutions are there to the equation below?
Studentka2010 [4]
No solution

3x+5+4x=7x+9
7x+5=7x+9
-7x -7x

you’re left with no x.. so no solution
6 0
2 years ago
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