Solving with Unlike Bases. Warm Ups on the next 3 slides….

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Presentation transcript:

Solving with Unlike Bases

Warm Ups on the next 3 slides….

Solve. Graph. Condense.

Warm Up

The Common Logarithm The base-10 logarithm is called the common logarithm. The common logarithm is usually written as logx. If we can manage to make everything into log base 10, we can use our calculators to solve.

For Example….Solve

Solve:

Change of Base There is a way to write equivalent logarithmic expressions with different bases. There is a formula to find the change of base. Let’s derive the change of base formula…..

Let’s derive the change of Base Formula!

Change of Base Formula:

Evaluate to the nearest hundredth.

Natural Log

Warm Up: Find the final amount of money if you invested $6700 compounded monthly at 5.4% for 20 years. $4500 compounded continuously at 7% for 20 years.

Warm Up: $1000 is invested at 15% per annum interest, compounded monthly. Calculate the minimum number of months required for the value of the investment to exceed $3000.

Warm Up:

Natural Base e = … Models a variety of situations of growth & decay in nature Represented as: ln (means log e )

Evaluate to the nearest thousandth.

Evaluate to the nearest thousandth. (Think of 2 Ways…….

Evaluate to the nearest thousandth.

Find

Simplify each expression.

Simplify each expression. (2 Ways)

Solve – Round to the nearest hundredth. (2 Ways)

Solve – Round to the nearest hundredth. (Use ln)

Solve – Round to the nearest hundredth.