Respuesta :
Answer:
0.48
Step-by-step explanation:
The problem at hand
[tex]500 = (2)(10^{5x})[/tex]
First divide out 2 on both side of the = sign
[tex]500 = (2)(10^{5x})[/tex]
[tex]\frac{500}{2} = \frac{(2)(10^{5x})}{2}[/tex]
[tex]250 = 10^{5x}[/tex]
Now take the base 10 log on each side of the = sign
[tex]\log_{10} (250) = \log_{10} (10^{5x})[/tex]
Now move the exponent to the left like so
[tex]\log_{10} (250) = 5x \log_{10} (10)[/tex]
Rule you need to know. [tex]\log_a (a) = 1[/tex]
[tex]\log_{10} (250) = 5x (\log_{10} (10))[/tex]
[tex]\log_{10} (250) = 5x(1)[/tex]
[tex]\log_{10} (250) = 5x[/tex]
Now divide 5 from both sides of the equation
[tex]\frac{\log_{10} (250)}{5} = \frac{5x}{5}[/tex]
[tex]\frac{\log_{10} (250)}{5} = x[/tex]
[tex]x = \frac{\log_{10} (250)}{5}[/tex]
[tex]x = 0.4795880017[/tex]
Round to nearest hundredths
[tex]x = 0.48[/tex]
Side Note:
You could approach this problem in a different manner.
For instance, we could have done the following
[tex]x = \frac{\log_{10} (250)}{5(\log_{10} (10))}[/tex]
Also, you did not have to use log with a base 10. You could have used the natural log, which is [tex]\ln_e (x)[/tex]
[tex]x = \frac{\ln_{e} (250)}{5(\ln_{e} (10))}[/tex]
