Given: log 2 = 0.3010

To Find: Value of log8^25

Solution:

We can use the following formula to solve the problem:

loga^n = nloga

So, we have:

log8^25 = 25log8

Now, we know that:

log8 = log(2^3)

Using the property of logarithms, we can write:

log8 = 3log2

Substituting the value of log2 in the above equation, we get:

log8 = 3(0.3010)

log8 = 0.9030

Substituting the value of log8 in the original equation, we get:

log8^25 = 25log8

log8^25 = 25(0.9030)

log8^25 = 22.575

Therefore, the value of log8^25 given log 2 = 0.3010 is 22.575.

Explanation:

To find the value of log8^25, we used the formula loga^n = nloga. We then simplified the expression by using the property of logarithms and substituted the value of log2 to find the value of log8. Finally, we substituted the value of log8 in the original equation to find the value of log8^25.