Question

Пожалуйста помогите решить,( Вычислить log5b^4, если log5 b=5) и если не трудно объесните как решать такие задачки, заранее спасибо)))

Answer 1

Log5b^4=4log5b=4*5=20
просто посмотри формулы на свойства логарифмов - если логарифмируемое выражение или число стоит в какой либо степени, эту степень выносим перед логарифмом как множитель и всё.

Answer 2

Solving log Equations

To solve the equation log5(b^4), given that log5(b) = 5, we can use the properties of logarithms. The key property we will use is that log_a(b^c) = c * log_a(b).

Solution Steps

1. Use the Property of Logarithms: We can use the property log_a(b^c) = c * log_a(b) to rewrite log5(b^4) as 4 * log5(b). 2. Substitute the Given Value: Since we know that log5(b) = 5, we can substitute this value into the expression. 3. Calculate the Result: After substituting the value of log5(b), we can calculate the result.

Calculation

Using the property of logarithms, we rewrite log5(b^4) as 4 * log5(b). Then, substituting the given value log5(b) = 5: log5(b^4) = 4 * log5(b) = 4 * 5 = 20.

So, log5(b^4) = 20.

Explanation

To solve such problems, it's important to understand the properties of logarithms. In this case, we used the property log_a(b^c) = c * log_a(b) to simplify the expression. Then, we substituted the given value of log5(b) to calculate the result.

I hope this helps! Let me know if there's anything else you'd like to discuss or any other questions you have.