Question

Решить 3^log27(5x+8)=6

Answer 1

Вот решение 192,7498578526719

Answer 2

To solve the equation 3^log27(5x + 8) = 6, we can use the property of logarithms that states:

If a^log_a(b) = b, then log_a(b) = 1.

First, let's rewrite the equation using this property:

3^log27(5x + 8) = 6 => log27(5x + 8) = log3(6)

Now, we can change the base of the logarithm using the change of base formula:

log_a(b) = log_c(b) / log_c(a)

Using this formula with base 27:

log27(5x + 8) = log3(6) / log3(27)

Since log3(27) = 3 (3 raised to what power equals 27?), we have:

log27(5x + 8) = log3(6) / 3

Now, we can rewrite the equation in exponential form:

27^(log27(5x + 8)) = 27^(log3(6)/3)

Since the base and logarithm cancel each other out, we get:

5x + 8 = 6^(1/3)

Now, calculate 6^(1/3):

6^(1/3) ≈ 1.8171

Now, solve for x:

5x + 8 = 1.8171

Subtract 8 from both sides:

5x = 1.8171 - 8

5x = -6.1829

Divide by 5:

x = -6.1829 / 5

x ≈ -1.2366

So, the solution to the equation is approximately x = -1.2366.