livsterdosewrk9233 livsterdosewrk9233
  • 15-01-2020
  • Mathematics
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Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.
e-0.5x = 0.075

Respuesta :

lisboa lisboa
  • 15-01-2020

Answer:

[tex]x=-\frac{ln(0.075)}{0.5}[/tex]

Step-by-step explanation:

[tex]e^{-0.5x}= 0.075[/tex]

To remove the base 'e' we take ln on both sides

[tex]e^{-0.5x}= 0.075[/tex]

[tex]ln(e^{-0.5x})=ln(0.075)[/tex]

As per log property we move the exponent before ln

[tex]-0.5xln(e)=ln(0.075)[/tex]

ln(e)=1

[tex]-0.5x=ln(0.075)[/tex]

divide by -0.5 on both sides

[tex]x=-\frac{ln(0.075)}{0.5}[/tex]

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