Evaluate 10 log of (10^-2)/(10^-12)

Problem

10*(log_)((10^(−2))/(10^(−12)))

Solution

1. Simplify the fraction inside the logarithm by using the quotient rule for exponents, a^m/a^n=a^(m−n)

(10^(−2))/(10^(−12))=10^(−2−(−12))

2. Calculate the exponent by performing the subtraction.

10^(−2+12)=10^10

3. Substitute the simplified expression back into the original logarithmic expression.

10*(log_)(10^10)

4. Apply the logarithm property (log_b)(b^x)=x assuming the base is 10.

(log_)(10^10)=10

5. Multiply the result by the coefficient 10.

10×10=100

Final Answer

10*(log_)((10^(−2))/(10^(−12)))=100

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