Calculation of x from log equation

In summary, the conversation discusses an equation and the process of solving for x by modifying the formula and using the value of y, A, and z. The correct formula is x=y*10^(A*e^(z(-1))). The use of log base 10 is noted as unusual in mathematics. It is suggested to use y in the calculation instead of 10^log(y) for simplicity.
  • #1
AligatorAmy
28
1
Hi

I have the following equation:
Log(x/y)=A*(e^z(-1))

I know values of y, A, z.
I need to calculate x from this equation.

I need to ‘extract’ x first therefore
Log(x)-Log(y)= A*(e^z(-1))
Log(x) = A*(e^z(-1)) +Log(y)
x=10^[ A*(e^z(-1)) +Log(y)]

I am not sure whether my formula modification is correct.
Please help.
Thanks.
 
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  • #2
It looks correct to me, assuming the base of the ## Log ## function is 10.
 
  • #3
Most of it is correct, but I am not sure of the line "x=10^[ A*(e^z(-1)) +Log(y)]". Using log10 is unusual in mathematics. Yes, I see that you do not write "ln(x/y)", but be sure to check what kind of logarithms you have.
 
  • #4
It would be simpler for calculation if you used y instead of 10^log(y), i.e. [tex]x=y\times 10^{A\times e^{z(-1)}}[/tex]
 
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FAQ: Calculation of x from log equation

1. How do you solve a logarithmic equation to find the value of x?

To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation in exponential form. Then, you can isolate the variable x by using algebraic techniques such as combining like terms and factoring. Finally, you can use a calculator or manual calculation to find the value of x.

2. What is the purpose of using logarithms to find the value of x?

Logarithms are used to solve equations in which the variable is in the exponent. By taking the logarithm of both sides of the equation, the variable can be moved to the front of the equation, making it easier to solve for its value.

3. Can a logarithmic equation have more than one solution for x?

Yes, a logarithmic equation can have multiple solutions for x. This is because logarithmic functions are not one-to-one, meaning that different inputs can produce the same output. When solving a logarithmic equation, it is important to check your answer to make sure it satisfies the original equation.

4. Are there any restrictions on the values of x in a logarithmic equation?

Yes, there are some restrictions on the values of x in a logarithmic equation. The argument of a logarithm must be positive, so any values of x that result in a negative or zero argument are not valid. Additionally, the base of the logarithm must be greater than 0 and not equal to 1.

5. Is it possible to solve a logarithmic equation without using logarithms?

Yes, it is possible to solve some logarithmic equations without using logarithms. For example, if the equation contains a single logarithm on both sides, you can simply set the arguments of the logarithms equal to each other and solve for x. However, in most cases, using logarithms is the most efficient and accurate method for solving logarithmic equations.

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