Logarithmic Equations - MathBitsNotebook(A2)

Logarithmic Equations
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A logarithmic equation can be solved using the properties of logarithms along with its inverse relationship with exponentials.

Properties of Logarithms:

To solve most logarithmic equations:

1. Isolate the logarithmic expression
(you may need to use the properties of logarithms to create one
logarithmic term).
2. Rewrite in exponential form (with a common base)
3. Use the inverse relationship with exponentials:

(where a > 0, a ≠1, and log_ax is defined).
4. Solve for the variable.
5. Check for possible extraneous solutions.
Remember the domain of logarithmic functions is x > 0.

Things to remember
about logs:

Remember that y = e^x and
y = ln x are inverse functions.

Solve for x:

Answer

• Take e of both sides to eliminate the ln
• Remember that e^x and ln x are inverse function (one undoes the other).

• Isolate the log expression

• Choose base 10 to correspond with log (base 10)

• Apply composition of inverses and solve.

• Choose base 5 to correspond with the log base of 5.

• Isolate the ln expression first.

• You will need to use the log properties to express the two terms on the left as a single term.

• Remember that log of a negative value is not a real number and is not considered a solution.

Using your graphing calculator, solve for x to the nearest hundredth.
Method 2: Place the left side of the equation into Y₁ and the right side into Y₂. Under the CALC menu, use #5 Intersect to find where the two graphs intersect.

Method 1: Rewrite so the equation equals 0.

Find the zeros of the function. loggraph

Both values are solutions, since both values allow for the ln of a positive value.

For help with logarithms on
your calculator,
click here.

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