Which exponent makes the statement true? 1/5 to the ninth power=5
The exponent that makes the statement true is -9.
When raising 1/5 to the power of -9, we get:
(1/5)^(-9) = 5
This is because any number raised to the power of -n is equal to its reciprocal raised to the power of n. So, (1/5)^(-9) can be rewritten as (5/1)^9 = 5^9/1^9 = 5^9 = 5.
To find the exponent that makes the statement true, we need to evaluate the expression 1/5 raised to the x-th power.
So let's find the value of 1/5 to the x-th power.
(1/5)^x = 5
To simplify this equation, we can convert 5 to a fraction with a denominator of 1:
(1/5)^x = 5/1
Now, we can rewrite 5 as a fraction with a denominator of 5:
(1/5)^x = 5/5
Simplifying further:
(1/5)^x = 1
To find the value of x, we need to determine what exponent will make 1/5 equal to 1.
Since any number raised to the power of 0 is equal to 1, we can conclude that x must be 0.
Therefore, the exponent that makes the statement true is 0.
To find the exponent that makes the statement true, we need to solve the equation:
(1/5)^n = 5
To do this, we can take the logarithm of both sides of the equation. Since the base of the exponent is 1/5, we'll use a logarithm with base 1/5.
log(1/5)^n = log(5)
Using the logarithm property that states log(x^a) = a*log(x), we can simplify the equation:
n*log(1/5) = log(5)
Now, we divide both sides of the equation by log(1/5) to solve for n:
n = log(5) / log(1/5)
Using a calculator, we can evaluate this expression:
n ≈ 9.57
Therefore, the exponent that makes the statement true is approximately 9.57.