Question

Log2 (8a) esli logxa= 0.2 reshite pozhaluista

Answer 1

$log _{2}8a=log _{2} 8+log _{2} a= log _{2} 2^{3} +log _{2}a=3log _{2}2+log _{2} a=3+0,2=$ $=3,2$

Answer 2

To solve the equation log2(8a) when logxa = 0.2, we can use logarithm properties to simplify the expression and find the value of 'a'.

Recall the logarithm property: log_b(x^y) = y * log_b(x)

In this case, we have: log2(8a) = log2(2^3 * a) (Since 8 = 2^3) = 3 * log2(2) + log2(a) = 3 * 1 + log2(a) (Since log2(2) = 1)

Now, we are given that logxa = 0.2, so:

0.2 = log2(a)

To isolate 'a', we need to convert the logarithmic equation to its exponential form:

a = 2^(0.2)

Now, let's calculate the value of 'a':

a ≈ 2^(0.2) a ≈ 1.148698354997035

Therefore, the approximate value of 'a' is 1.1487 (rounded to four decimal places).