Evaluate log b {square root of 10b}, given that log b 2 = 0.3562 and

log b 5 = 0.8271 (sorry I had no clue how to type this in math format!)

I saw the question this way

logb (√(10b))
= 1/2(logb(10b))
= 1/2(logb5 + logb2 + logbb)
= 1/2(.8271 + .3562 + 1)
= 1.0917

The second answer is the correct answer! Thanks to you both I am on my way to the final

Shellie

I am not sure if I interpret your question correctly.

Given logb2 = 0.3562 and
logb5 = 0.8271,
evaluate logb{square-root of 10b};

logb{square-root of 10b}
= logb{square-root of 2b*5b}
=(1/2)logb(10b)
=(1/2)(1)
=0.5
since logb10b = b for any b.
However, if the number 10 is replaced by 10 to the base 10, we proceed slightly differently:
logb{square-root of 10}
=(1/2)logb(10)
= (1/2)logb(2*5)
= (1/2)(logb(2)+logb(5))
= (1/2)(0.3562+0.8271)
=0.5916

No problem! I can help you with that. To evaluate the expression log_b(square root of 10b), we can use the properties of logarithms.

First, let's take a look at the expression inside the logarithm: the square root of 10b. We can rewrite it as (10b)^(1/2), using the property of square roots that says taking the square root is the same as raising to the power of 1/2.

Now, applying the logarithmic property log_b(a^m) = m * log_b(a), we have:

log_b(square root of 10b) = log_b((10b)^(1/2))
= (1/2) * log_b(10b)

Next, let's simplify the expression log_b(10b). We can use the logarithmic property log_b(xy) = log_b(x) + log_b(y) to break it down:

log_b(10b) = log_b(10) + log_b(b)

Using this property, we need to find log_b(10) and log_b(b). Luckily, we're given log_b(2) and log_b(5), so we can use these values.

Using the property log_b(x^n) = n * log_b(x), we can express log_b(10) as log_b(2 * 5):

log_b(10) = log_b(2 * 5)
= log_b(2) + log_b(5)
= 0.3562 + 0.8271

Now, we can substitute the values into the original expression:

log_b(square root of 10b) = (1/2) * log_b(10b)
= (1/2) * (log_b(10) + log_b(b))
= (1/2) * (0.3562 + 0.8271)

Evaluating this expression, we get:

log_b(square root of 10b) = (1/2) * (0.3562 + 0.8271)
= 0.59165

Therefore, the value of log_b(square root of 10b) is approximately 0.59165.