Question

Log с основанием 2/3 (-x)=1

Answer 1

$log_{ \frac{2}{3} }( - x) = 1 \\ - x = { (\frac{2}{3}) }^{1} \\ - x = \frac{2}{3} \\ x = - \frac{2}{3}$

Answer 2

To solve the logarithmic equation, we need to get rid of the logarithm first. To do that, we'll use the property of logarithms which states:

log_b(a) = c is equivalent to b^c = a

In this case, the given equation is:

log(2/3, -x) = 1

Using the property mentioned above, we get:

(2/3)^1 = -x

Now, simplify the left side:

2/3 = -x

To solve for x, we need to isolate it. Multiply both sides by -1 to get x by itself:

x = -(2/3)

So, the solution to the equation is:

x = -2/3