Question

quadratic quations with logarithms

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Answer 1

Step-by-step explanation:

Start by condensing the log expressions on the left into a single logarithm using the Product Rule. What we want is to have a single log expression on each side of the equation. Be ready though to solve for a quadratic equation since x will have a power of 2. Solve the quadratic equation using the factoring method.

Answer 2

Answer:

Solving Logarithmic Equations

Generally, there are two types of logarithmic equations. Study each case carefully before you start looking at the worked examples below.

Types of Logarithmic Equations

   The first type looks like this.

If you have a single logarithm on each side of the equation having the same base then you can set the arguments equal to each other and solve. The arguments here are the algebraic expressions represented by M\color{blue}MM and N\color{red}NN.

   The second type looks like this.

If you have a single logarithm on one side of the equation then you can express it as an exponential equation and solve.

Let’s learn how to solve logarithmic equations by going over some examples.

Examples of How to Solve Logarithmic Equations

Example 1: Solve the logarithmic equation.

Solving Literal Equations Problem #3 Video

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Since we want to transform the left side into a single logarithmic equation, then we should use the Product Rule in reverse to condense it. Here is the rule just in case you forgot.

   Given

   Apply Product Rule from Log Rules.

   Distribute: (x+2)(3)=3x+6\left( {x + 2} \right)\left( 3 \right) = 3x + 6(x+2)(3)=3x+6

   Drop the logs, set the arguments (stuff inside the parenthesis) equal to each other.

   Then solve the linear equation. I know you got this part down!

Just a big caution. ALWAYS check your solved values with the original logarithmic equation.

Remember:

   It is OKAY to have values of xxx such as positive, 000, and negative numbers.

   However, it is NOT ALLOWED to have a logarithm of a negative number or a logarithm of zero, 000, when substituted or evaluated into the original logarithm equation.

⚠︎ CAUTION: The logarithm of a negative number, and the logarithm of zero are both not defined.

log⁡b(negative  number)=undefined{\log _b}\left( {{\rm{negative\,\,number}}} \right) = {\rm{undefined}}logb​(negativenumber)=undefined

log⁡b(0)=undefined{\log _b}\left( 0 \right) = {\rm{undefined}}logb​(0)=undefined

Hope this helps you mate :) :) :)