How does 1=5.85e^(-x/(5*10^-5)) become e^(x/(5*10^-5))=5.85? This confusion I don't how this could be possible.
5.85=e^(-x/5×10^-5)
5.85e^[(-x)(1/(5×10^-5)]=1
When you have something like 2^(-1)=1/2
Using that idea above
5.85/e^(x)(1/(5×10^-5)]=1/1
Cross multiply
5.85=e^(x)(1/(5×10^-5)]
Do you understand?
Assuming you have
e^(-x)=1
1/e^x=1/1
Cross multiply it is basic maths
1×1=e^x×1
e^x=1
Got the ideal??
No, can you show step by step using the giving number instead?
Thank you,
I understand. I haven't use this type of math for many years so I forgot but you refresh my memory.
You're welcome
To understand how the equation 1 = 5.85e^(-x/(5*10^-5)) becomes e^(x/(5*10^-5)) = 5.85, let's go step by step.
Step 1: Start with the given equation: 1 = 5.85e^(-x/(5*10^-5)).
Step 2: Divide both sides of the equation by 5.85 to isolate the exponential term:
1/5.85 = e^(-x/(5*10^-5)).
Step 3: Take the natural logarithm (ln) of both sides of the equation. The natural logarithm is the inverse function of the exponential function:
ln(1/5.85) = ln(e^(-x/(5*10^-5))).
Step 4: Use the property of logarithms that states ln(e^a) = a:
ln(1/5.85) = -x/(5*10^-5).
Step 5: Simplify the left side of the equation using the property ln(1/a) = -ln(a):
-ln(5.85) = -x/(5*10^-5).
Step 6: Multiply both sides by -1 to get rid of the negative sign:
ln(5.85) = x/(5*10^-5).
Step 7: Multiply both sides by (5*10^-5) to isolate x:
(5*10^-5) * ln(5.85) = x.
Step 8: Rewrite the equation to match the desired form e^(x/(5*10^-5)) = 5.85:
e^(x/(5*10^-5)) = 5.85.
By following these steps, we have transformed the original equation 1 = 5.85e^(-x/(5*10^-5)) into the form e^(x/(5*10^-5)) = 5.85. It's important to note that mathematical transformations like this involve applying various algebraic operations to both sides of the equation while following the rules of arithmetic and algebra.