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The equation you have provided is log(1/1000000) = -6.
To understand this equation, we need to know what the logarithm function is. The logarithm, often written as log, is the opposite operation of exponentiation. It helps us solve for the power to which a base number must be raised to obtain a given value.
In this equation, the base of the logarithm is not mentioned explicitly, but the common base in mathematics is 10 unless otherwise specified. So, by default, we assume the base of the logarithm to be 10.
To further explain the equation, we need to evaluate log(1/1000000). The fraction 1/1000000 can be simplified to 1 over 10 to the power of 6 (which is 1 divided by 1,000,000, which is the same as saying 1 divided by 10 raised to the power of 6).
So, log(1/1000000) can be rewritten as log(1) - log(10^6), where log(1) is 0 since any number raised to the power of 0 is always 1 and log(10^6) is 6 since 10^6 is 1,000,000.
Simplifying further, we have log(1) - log(10^6) = 0 - 6 = -6. Therefore, log(1/1000000) equals -6.
Logarithms are frequently used in various fields such as mathematics, science, and engineering. They allow us to solve problems involving exponential growth or decay, such as compound interest calculations, population growth, and radioactive decay. Logarithms also provide a way to represent multiplicative relationships as additive relationships, making calculations more manageable. It's important to understand logarithms and their properties to solve equations and analyze data effectively.