Solution:

Given, log(a^9) = 10

We need to find the value of 'a'.

We know that, log(a^n) = n * log(a)

Using this property, we can write the given equation as:

9 * log(a) = 10

Dividing both sides by 9, we get:

log(a) = 10/9

Taking antilogarithm on both sides, we get:

a = 10^(10/9)

Therefore, the value of 'a' is 10^(10/9).

Explanation:

To solve this problem, we have used the properties of logarithms. The basic idea behind logarithms is that they help us to convert multiplication and division into addition and subtraction. This makes it easier to perform complex mathematical operations.

In this particular problem, we have used the property of logarithms which states that the logarithm of a power of a number is equal to the product of the exponent and the logarithm of the base. Using this property, we have simplified the given equation and obtained an expression for 'log(a)'.

To obtain the value of 'a', we have used the antilogarithm property, which states that the antilogarithm of a logarithm is equal to the original number. Using this property, we have obtained the value of 'a' in terms of 10.

Overall, this problem requires a good understanding of logarithms and their properties. With practice, one can become proficient in solving such problems.