# Algebra II : Solving and Graphing Logarithms

## Example Questions

### Example Question #11 : Solving Logarithms

Evaluate .

No solution

Explanation:

In logarithmic expressions,  is the same thing as

Therefore, the equation can be rewritten as .

Both 8 and 128 are powers of 2, so the equation can then be rewritten as .

Since both sides have the same base, set .

Solve by dividing both sides of the equation by 3: .

### Example Question #12 : Solving Logarithms

Solve the equation for .

No solution

Explanation:

Because both sides have the same logarithmic base, both terms can be set equal to each other:

Now, evaluate the equation.

First, add x to both sides:

Finally, divide by 6: .

### Example Question #1 : Solving Logarithmic Functions

Solve this logarithmic equation:

Explanation:

To solve this problem you must be familiar with the one-to-one logarithmic property.

if and only if x=y. This allows us to eliminate to logarithmic functions assuming they have the same base.

one-to-one property:

isolate x's to one side:

move constant:

### Example Question #2 : Solving Logarithmic Functions

Solve the equation:

No solution exists

Explanation:

Get all the terms with e on one side of the equation and constants on the other.

Apply the logarithmic function to both sides of the equation.

### Example Question #11 : Solving And Graphing Logarithms

Solve the equation:

Explanation:

Recall the rules of logs to solve this problem.

First, when there is a coefficient in front of log, this is the same as log with the inside term raised to the outside coefficient.

Also, when logs of the same base are added together, that is the same as the two inside terms multiplied together.

In mathematical terms:

Thus our equation becomes,

To simplify further use the rule,

.

### Example Question #13 : Solving Logarithms

Solve for

Explanation:

Logarithms are another way of writing exponents. In the general case,  really just means . We take the base of the logarithm (in our case, 2), raise it to whatever is on the other side of the equal sign (in our case, 4) and set that equal to what is inside the parentheses of the logarithm (in our case, x+6). Translating, we convert our original logarithm equation into . The left side of the equation yields 16, thus .

### Example Question #12 : Solving Logarithmic Functions

Explanation:

To solve this equation, remember log rules

.

This rule can be applied here so that

and

### Example Question #161 : Logarithms

Explanation:

To solve this equation, you must first simplify the log expressions and remember log laws (; ). Therefore, for the first expression, so . For the second expression, so  Then, substitute those numbers in so that you get .

### Example Question #162 : Logarithms

Solve for

Explanation:

Remember that a logarithm is nothing more than an exponent. The equation reads, the logarithm (exponent) with base  that gives  is

### Example Question #163 : Logarithms

Solve the equation