Answer :
Final answer:
To evaluate the logarithmic function log5 230 = x, apply the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. By rewriting the equation and simplifying, x is found to be equal to 1.
Explanation:
To evaluate the logarithmic function log5 230 = x, we can use the property of logarithms that states: the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. In this case, we can rewrite 230 as 5 raised to some power:
230 = 5x
Now we can take the logarithm of both sides using base 5:
log5 230 = log5 (5x)
By the property mentioned earlier, we can rewrite the right-hand side as:
x * log5 5
Since log5 5 = 1, we have:
x * 1
Therefore, the value of x is simply equal to:
x = 1
The value of x in the given logarithmic function is: x = 3.379
How to identify properties of logarithm?
There are different properties of Logarithm such as:
Product property
Quotient property
Power property
Change of base property
From properties of logarithm, we know that:
If logₐ m = x
Then: m = aˣ
Thus:
log₅230 = x gives us:
5ˣ = 230
x In 5 = In 230
x = 3.379
Read more about Properties of Logarithm at: https://brainly.com/question/12049968
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