Question

5^2+log5 10 5-внизу под log 10-на уровне с log 2-тоже на уровне с log

Answer 1

$5^{2+log_510}=5^2*5^{log_510}=25*10=250$

Answer 2

Let's break down the expression step by step:

1. 5^2: This simply means 5 raised to the power of 2, which is equal to 5 * 5 = 25.

2. log5(10): This represents the logarithm of 10 to the base 5. We can express this in a different base using the change of base formula for logarithms, which states that log_a(b) = log_c(b) / log_c(a), where "c" can be any positive base, typically 10 or e (natural logarithm).

Since we want to find log_5(10), let's use the base 10 logarithm:

log_5(10) = log_10(10) / log_10(5) = 1 / log_10(5)

3. 5 - log(10, 5): This simply means 5 minus the logarithm of 5 to the base 10. Again, we can use the change of base formula to express this in a different base. Let's use the natural logarithm (base e) this time:

5 - log_10(5) = 5 - (log_e(5) / log_e(10)) = 5 - (ln(5) / ln(10))

4. log(2, log(10, 5)): This means the logarithm of 5 to the base 10, and then taking the logarithm of that result to the base 2. Let's perform these calculations step by step:

log_10(5) = log_e(5) / log_e(10) = ln(5) / ln(10)

Now, taking the logarithm of the above result to the base 2:

log_2(log_10(5)) = log_2(ln(5) / ln(10))

So, the final expression is:

25 + (1 / log_10(5)) - (5 - (ln(5) / ln(10))) - log_2(ln(5) / ln(10))

Please note that this expression involves both logarithmic and algebraic calculations, and you may use a calculator to get the numerical value.