Unit 5!

 
In this unit we will be discussing Expanding logarithmic functions, condensing logarithmic functions, solving exponential and logarithmic equations

When expanding logarithms we must take into account of the different rules that come with it.

Step 1: Write the equation

log6(5x^3/y)

Step 2: Quotient, Product, Equality, & Change of base rules.

Note: When there is division in the logarithm then you must subtract the log of the divisor from the log of the dividend, when using multiplication you add both logs.

log6(5) + log6(x^3) - log6(y)

As you can see here we're literally just expanding the equation by attaching log6() to every piece

Step 3: Power Rule

When using this property, you move any exponent to the front of the variable by which the exponent is attached to

log6(x^3) = 3log6(x)

Step 4: Write out final expanded equation

log6(5) + 3log6(x) - log6(y)