Question

найти значение выражения log числа0,25 основание 32, 18 log числа 7 основание корень шестой степени из 7

Answer 1

log(32)0.25=log(2^5)2^(-2)=-2/5*log(2)2=-2/5

log(корень 6 степени 7)7=log(7^1/6)7=6*log(7)7=6

Answer 2

log(0.25) base 32:

To find the value of log(0.25) with a base of 32, we need to determine the exponent to which we need to raise the base (32) to get the number (0.25).

Let's express 0.25 as a fraction: 0.25 = 1/4.

So, log(0.25) base 32 is the exponent to which we have to raise 32 to obtain 1/4.

To solve this, we can rewrite the equation as:

32^x = 1/4

To simplify further, we can express 1/4 as a power of 2:

32^x = 2^-2

Now, we can equate the exponents:

x = -2

Therefore, the value of log(0.25) base 32 is -2.

18 log(7) base (the 6th root of 7):

To find the value of 18 log(7) with a base of the sixth root of 7, we need to determine the exponent to which we need to raise the base (the sixth root of 7) to get the number 7.

The sixth root of 7 can be expressed as (7^(1/6)).

So, 18 log(7) base (the sixth root of 7) is the exponent to which we have to raise the sixth root of 7 to obtain 7.

To solve this, we can rewrite the equation as:

(7^(1/6))^x = 7

Simplifying further, we can equate the exponents:

(1/6) * x = 1

Multiplying both sides by 6:

x = 6

Therefore, the value of 18 log(7) base (the sixth root of 7) is 6.