Calculation of logarithms is an important concept in mathematics. In this question, we are asked to calculate the value of three logarithmic expressions. Let's solve them one by one.

Log 8 to the base 3:

We need to find the value of log 8 to the base 3. We know that log a to the base b is the power to which b must be raised to get a. So, we can write:

log 8 to the base 3 = n (let's assume)

This means that 3^n = 8

We know that 8 can be written as 2^3. So, we can write:

3^n = 2^3

Taking log on both sides, we get:

n*log 3 = 3*log 2

n = 3*log 2 / log 3

Therefore, log 8 to the base 3 = 3*log 2 / log 3

Log 16 to the base 9:

Similarly, we need to find the value of log 16 to the base 9. We can write:

log 16 to the base 9 = m (let's assume)

This means that 9^m = 16

We know that 16 can be written as 2^4. So, we can write:

9^m = 2^4

Taking log on both sides, we get:

m*log 9 = 4*log 2

m = 4*log 2 / log 9

Therefore, log 16 to the base 9 = 4*log 2 / log 9

Log10 to the base 4:

Finally, we need to find the value of log10 to the base 4. We can write:

log10 to the base 4 = p (let's assume)

This means that 4^p = 10

We can use the change of base formula to solve this expression. According to the formula:

log a to the base b = log a / log b

So, we can write:

log10 to the base 4 = log 10 / log 4

Using a calculator, we get:

log10 to the base 4 = 1.66096

Therefore, log10 to the base 4 = 1.66096

In summary, we have calculated the value of three logarithmic expressions using the basic concepts of logarithms and the change of base formula.

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