Final answer:
The equation 10 to the power of negative four equals 0.0001 is expressed in logarithmic form as log base 10 of 0.0001 equals negative 4.
Step-by-step explanation:
To express the equation 10-4 = 0.0001 in logarithmic form, you need to understand the relationship between exponents and logarithms. The exponent in the original equation indicates how many times 10 is multiplied by itself to get 0.0001. In logarithmic form, this will be written as log10(0.0001) = -4.
Here's a step-by-step explanation:
- Recognize that 10-4 means 10 is raised to the power of -4.
- Recall that logarithmic form translates the equation from exponential form, where a number (the base) raised to a power equals a value, into the form where we're looking for the exponent itself given the base and value.
- Substitute the known quantities into the logarithmic equation: Since 10n = value, then logb(value) = n, where b is the base and n is the exponent.
- Apply this to the original equation: Since 10-4 = 0.0001, then log10(0.0001) = -4.