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, am/an=a(m−n)

(10(−2))/(10(−12))=10(−2−(−12))

2. Calculate the exponent by performing the subtraction.

10(−2+12)=10

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

10*(log_)(10)

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

(log_)(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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