9/5 log to the base 3 (x)= -7
solve for x
To solve for x, you need to isolate it on one side of the equation. In this case, we have:
(9/5) log₃(x) = -7
First, let's get rid of the fraction by multiplying both sides of the equation by 5:
5 * (9/5) log₃(x) = 5 * (-7)
This simplifies to:
9 log₃(x) = -35
Next, divide both sides of the equation by 9:
(9 log₃(x)) / 9 = -35 / 9
This results in:
log₃(x) = -35/9
Now, we can solve for x by expressing the equation in exponential form. In logarithmic form, log₃(x) = y can be rewritten as 3^y = x.
So, applying that to our equation:
3^(-35/9) = x
Therefore, x ≈ 0.1205 (rounded to four decimal places).