Final answer:
To calculate loga (30a)³, apply the power and product rules of logarithms, resulting in 4.4305 + 3 × log10 a.
Step-by-step explanation:
The value of loga (30a)^3 can be found by applying the power rule of logarithms, which states that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.
Using the power rule of logarithms, loga (30a)³ can be simplified as follows:
loga (30a)³ = loga (30³ × a³)
= loga (27000 × a³)
= loga 27000 + loga a³
= loga 27000 + 3 × loga.a
= log10 27000 + 3 × log10 a (since loga x = log10 x / log10 a)
= 4.4305 + 3 × log10 a
Therefore, loga (30a)³ = 4.4305 + 3 × log10 a