Question

Find the numerical value of the log expression loga=7logb=-12logc=-6 log(a⁹b⁹c²)

Answer 1

The value of the logarithmic expression log(a⁹b⁹c²) given log(a) = 7, log(b) = -12, and log(c) = -6 is -57, after applying the properties of logarithms.

Step-by-step explanation:

The student is asking how to find the numerical value of the logarithmic expression log(a⁹b⁹c²) with the given values of log(a) = 7, log(b) = -12, and log(c) = -6. Using logarithmic properties, we can expand the expression as follows:

• log(a⁹b⁹c²) = 9*log(a) + 9*log(b) + 2*log(c)
• log(a⁹b⁹c²) = 9*7 + 9*(-12) + 2*(-6)
• log(a⁹b⁹c²) = 63 - 108 - 12
• log(a⁹b⁹c²) = -57

Therefore, the numerical value of the logarithmic expression is -57.