We know that
Remember the rule of exponents:
#(a^b)^c = a^(bc)#
#(color(red)(5^-x))^(-3) = 5^((-x)(-3)) = 5^(3x)#
So we need to raise
#(color(red)(5^-x))^(-3) = color(blue)3^(-3) = 1/color(blue)3^3 = 1/27#
In order to solve this, you can use a calculator or just use
However....if you don't know what
This might seem a little confusing at first, but the a is the "base". B is supposed to be the exponent of a in order to get
An actual example:
As you could see, 5 is the
Rule: If there is no base or a, then the a value is automatically assumed to be 10.
Now, another essential rule is that if a^b has an actual exponent on it (such as
Now, let's multiply the result by two...
Let's multiply the result by two...
As you can see here,
Then, due to the rules of logarithms, we can move the power of the
Divide both sides by
Then multiply both sides by negative one to get:
Now that we know what x is, we can plug it into the equation to get...
You can simplify the logs with a calculator in order to get 0.37037....
Forgive me for this long answer.