Solving Exponential equations using logs

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.

Front

How do you solve an exponential equation using logarithms?

Back

To solve an exponential equation using logarithms, you can take the logarithm of both sides of the equation. This allows you to bring the exponent down and solve for the variable.

Front

What is the logarithmic form of an exponential equation?

Back

The logarithmic form of an exponential equation a^b = c is log_a(c) = b, where a is the base, b is the exponent, and c is the result.

Tags

CCSS.HSF.BF.B.5

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_a(b) = log_c(b) / log_c(a) for any positive c, allowing you to compute logarithms with different bases.

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

What is the common logarithm?

Back

The common logarithm is the logarithm to the base 10, denoted as log(x). It is often used in scientific calculations.

Front

How do you round a number to two decimal places?

Back

To round a number to two decimal places, look at the third decimal place. If it is 5 or greater, round up the second decimal place by one. If it is less than 5, keep the second decimal place the same.

Tags

CCSS.5.NBT.A.4

Front

What is the significance of the base in an exponential equation?

Back

The base in an exponential equation determines the rate of growth or decay. A base greater than 1 indicates exponential growth, while a base between 0 and 1 indicates exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the process to isolate the variable in an exponential equation?

Back

To isolate the variable in an exponential equation, you may need to use logarithms, rearranging the equation, and applying inverse operations to solve for the variable.

Front

What does it mean to solve for x using logs?

Back

Solving for x using logs means applying logarithmic properties to rewrite the exponential equation in a form that allows you to isolate and find the value of x.