m= M + 5 log(d/10)=18+5 x log(5/10)=
To solve this equation, you can follow these steps:
Step 1: Simplify the equation using the properties of logarithms.
- Rewrite the equation as: m = M + 5log(d/10) = 18 + 5log(5/10).
- Use the properties of logarithms to simplify the expression further.
- Recall that log(a/b) = log(a) - log(b). Apply this property to the equation:
m = M + 5(log(d) - log(10)) = 18 + 5(log(5) - log(10)).
Step 2: Simplify the logarithmic expressions.
- Log(10) is equal to 1, so log(10) = 1.
- Log(5) is equal to log(10/2), which we can further simplify.
- Using the property log(a/b) = log(a) - log(b), we get log(10) - log(2), which equals 1 - log(2).
- Therefore, log(5) = 1 - log(2).
Step 3: Substitute the simplified logarithmic expressions back into the equation.
- Now that we have simplified forms for log(10) and log(5), we can substitute them back into the equation:
m = M + 5(1 - log(2)) = 18 + 5(1 - log(2)).
Step 4: Perform the necessary arithmetic calculations.
- Continue simplifying the equation by applying the distribution property: 5(1 - log(2)) = 5 - 5log(2).
- Substitute this back into the equation:
m = M + 5 - 5log(2) = 18 + 5 - 5log(2).
Step 5: Combine like terms.
- Combine the constants on the right side of the equation: 18 + 5 = 23.
- Combine the logarithmic term as well: -5log(2).
- Therefore, the final equation becomes:
m = M + 23 - 5log(2).
Now, you have the simplified equation for m in terms of M.