Logarithmic Function Equation Examples

Log 7 49 2.

Logarithmic function equation examples. 53 5 5 5 25 5 125 means take the base 5 and multiply it by itself three times. If 2 log x 4 log 3 then find the value of x. Start by condensing the log expressions on the left into a single logarithm using the product rule. Therefore 7 2 64 in logarithmic function is.

Verify your answer by substituting it in the original logarithmic equation. Log 4 3 x 2 2. This problem does not need to be simplified because there is only one logarithm in the problem. X 7 x 7 checks we have a solution at.

Rewrite the equation in exponential form as. But as you know e 2 718281828. When no base is written assume that the log is base 10. Log 6 36 2.

And argument 125. Log 3 x 2 3 2 x x 9. X 1 1000 1 100 1 10 1 10 100 1000 y logx 3 2 1 0 1 2 3. The logarithmic function y logb x can be shifted k units vertically and h units horizontally with the equation y logb x h k.

Solve the logarithmic equation log 2 x 1 log 2 x 4 3. Color blue x 7 x 7. Log 3x5 log 7x12 3x57x 12 3x57x 12 17 x 4 17 x 4. Log 10 2 x 499 5 1 log 10 1000 3 since 10 3 1000.

Log 3 x log 3 x 6 3. 5 3 125 log 5 125 3. Write the logarithmic equivalent of 5 3 125. The logarithmic equations in examples 4 5 6 and 7 involve logarithms with different bases and are therefore challenging.

For the logarithm to be defined the only solution is 3. Log y 8 3. Log 7 49 y. Solve the logarithmic equation log 2 x 1 5.

Solve log x 4x 3 2. Rewrite each exponential equation in its equivalent logarithmic form. What we want is to have a single log expression on each side of the equation. Here are some examples.

Solve for x in log 3 x 2. 2 2 2 2 2 4 2 2 2 8 2 2 16 2 32. Ln 4x 1 3 4x 3 e 3. Log x 4x 3 2 x 2 4x 3 x 2 4x 3 0 x 1 x 3 0 so x 1 or 3.

Log 4 y 2. For 25 we take the 2 and multiply it by itself five times like this. Solve the following equations if possible. Rewrite each logarithmic equation in its equivalent exponential form.

Log 3 x 2 3 2 x x 9. Solve log 3 x 2. Evaluate ln 4x 1 3. 4x 3 2 718281828 3 20 085537.

Ln 3x11 4 this problem contains terms without logarithms. Log a m p. How to solve a logarithmic equation using properties of logarithms. 5 2 25.

To solve an equation involving logarithms use the properties of logarithms to write the equation in the form log bm n and then change this to exponential form m b n.