PrU3L5 Solving Natural Logarithmic equations e and ln

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To expand logarithms, you can use the following rules:

1. Product rule: The product rule of logarithms states that log base b of (x * y) is equal to the sum of log base b of x and log base b of y. Therefore, to expand a logarithm of a product, you can split it into the sum of logarithms of each factor. For example:

log base 2 of (x * y) = log base 2 of x + log base 2 of y

2. Quotient rule: The quotient rule of logarithms states that log base b of (x / y) is equal to the difference of log base b of x and log base b of y. Therefore, to expand a logarithm of a quotient, you can split it into the difference of logarithms of the numerator and denominator. For example:

log base 2 of (x / y) = log base 2 of x - log base 2 of y

3. Power rule: The power rule of logarithms states that log base b of (x^y) is equal to y times log base b of x. Therefore, to expand a logarithm of a power, you can multiply the exponent by the logarithm of the base. For example:

log base 2 of (x^3) = 3 * log base 2 of x

4. Change of base formula: The change of base formula allows you to change the base of a logarithm. It states that log base b of x can be expressed as log base a of x divided by log base a of b. Therefore, to expand a logarithm with a different base, you can use the change of base formula to express it in terms of a logarithm with a known base. For example:

log base 2 of x = log base 10 of x / log base 10 of 2

It's important to remember that when expanding logarithms, you may need to simplify or combine terms afterwards to get the expression into a more useful or simplified form.

[roxyxvr]

I learned what properties to apply to solve a natural logarithmic equation.

[llenigarcia]

I learned that there are four different properties of logarithms. When solving natural logarithms e cables out Ln and the point of solving is to try and figure out if the number does actually equal itself when you check it. If you have a fraction it is a good idea to cross multiply to make it easier.

[nathaliesanabria]

When dealing with fractions you should cross multiply to simplify the answer. Also, it is good to know that the e and ln will always cancel each other out.

[janesxa]

I learned how to use ln to solve logarithmic equations and to check the answer in an easy way.

[The_Dong]

I learned to use product properties when solving Natural logarithmic Equations. I also learned that ln will always cancel out with e.

[jarelynmanrique]

When solving natural logarithic the (ln) cancels out with the (e).

[yarithzasalgado]

I learned that there are 4 properties. And that they end up canceling eachother out. Also I learned the e cancels out the ln.