The Properties of Logarithms allow expressions with logarithms to be rewritten.
Simplify the expression using the properties of logarithms.
The Change of Base Formula allows the logarithm of an arbitrary base to be rewritten as the quotient of two logarithms with another base. With many calculators it is only possible to evaluate the common and the natural logarithm. The Change of Base Formula can then be used to evaluate logarithms of other bases.
First, the equation is rewritten by applying a logarithm on both sides.
By using the Power Property of Logarithms, powers can be rewritten into a product.
After the power has been rewritten into a product, the unknown variable can be isolated using inverse operations. Here, gets isolated on the left-hand side when both sides of the equation are divided by By using a calculator, an approximate value of can be calculated. Here,
Solve the equation using the common logarithm. State the answer with three significant digits.
These properties together with other properties of logarithms permit to simplify logarithmic expressions and to solve equations involving logarithms and powers. Some particular examples are shown below.
Solve the equation using the inverse properties of logarithms.