ln (x^r) =
To solve this equation, let’s first understand what the notation ln represents
To solve this equation, let’s first understand what the notation ln represents.
ln refers to the natural logarithm function, which is the inverse of the exponential function e^x. In other words, for any positive number y, ln(y) gives the exponent x such that e^x = y.
Now, let’s apply this understanding to the equation in question: ln(x^r). Here, x^r denotes x raised to the power of r. To simplify this expression using logarithmic rules, we can apply the power rule, which states that the logarithm of a number raised to an exponent is equal to the exponent multiplied by the logarithm of the number.
Hence, we can rewrite ln(x^r) as r * ln(x):
ln(x^r) = r * ln(x)
So, the equation ln(x^r) is equivalent to r * ln(x).
It’s worth mentioning that when solving equations involving a logarithm, you may want to isolate the logarithmic term on one side and then use exponentiation with the base of the logarithm to eliminate the logarithm itself. However, in this case, since ln(x^r) is already simplified to r * ln(x), no further manipulation is required.
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