nmomma83
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(Need asap)Solve each equation. Use one of the 4 methods you have practiced the last few days:
1. Write exponents using the same base
2. Take the log of both sides
3. Use properties of logs then write as an exponent
4. Use properties of logs then drop the log on both sides

13. 10e^8x+1 -3=70

Respuesta :

sqdancefan

Answer:

  x ≈ 0.123484

Step-by-step explanation:

You want the solution to the equation ...

  [tex]10e^{8x+1}-3=70[/tex]

Exponential

Essentially, you want to "undo" what is done to the variable. First of all, this means isolating the exponential term.

  [tex]10e^{8x+1}=73\qquad\text{add 3}\\\\e^{8x+1}=7.3\qquad\text{divide by 10}[/tex]

Logs

Now, you can take the log of both sides and solve the remaining 2-step linear equation.

  [tex]8x+1=\ln(7.3)\qquad\text{take the natural log of both sides}\\\\8x = \ln(7.3)-1\qquad\text{subtract 1}\\\\x=\dfrac{\ln(7.3)-1}{8}\qquad\text{divide by 8}\\\\\boxed{x\approx0.123484}\qquad\text{evaluate}[/tex]

Ver imagen sqdancefan
msm555

Answer:

x ≈ 0.12348

Step-by-step explanation:

To solve the equation [tex]10e^{8x+1} - 3 = 70[/tex], follow these steps:

Isolate the exponential term:

Add 3 to both sides to isolate the exponential term.

[tex]10e^{8x+1} = 70 + 3[/tex]

[tex]10e^{8x+1} = 73[/tex]

Divide both sides by 10:

[tex]e^{8x+1} = \dfrac{73}{10}[/tex]

Take the natural logarithm (ln) of both sides to eliminate the exponential term:

[tex]\ln(e^{8x+1}) = \ln\left(\dfrac{73}{10}\right)[/tex]

[tex]8x + 1 = \ln\left(\dfrac{73}{10}\right)[/tex]

Solve for [tex]x[/tex]:

[tex]8x = \ln\left(\dfrac{73}{10}\right) - 1[/tex]

[tex]x = \dfrac{1}{8} \left(\ln\left(\dfrac{73}{10}\right) - 1\right)[/tex]

Using calculator, we get:

[tex] x \approx 0.1234842935 [/tex]

[tex] x \approx 0.12348 \textsf{ in 5 d.p.)}[/tex]

Therefore, x ≈ 0.12348

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