# How to find x if 11^(2x+1)=13.

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The equation 11^(2x+1)=13 has to be solved for x.

11^(2x+1)=13

Take the logarithm of both the sides

`log(11^(2x+1))= log 13`

Use the property of logarithm `log a^b = b*log a`

`(2x +1)*log 11 = log 13`

Isolate x to one of the sides

`2x + 1 = (log 13)/(log 11)`

`2x = (log 13)/(log 11) - 1`

`x = ((log 13)/(log 11) - 1)/2`

The solution of the given equation is x = `((log 13)/(log 11) - 1)/2`

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To find out x, we'll take natural logarithms on both sides:

ln 11^(2x+1) = ln 13

We'll use the power rule of logarithms:

(2x+1)*ln 11 = ln 13

We'll divide by ln 11 both sides of the equation:

(2x+1) = ln 13 /ln 11

We'll subtract 1  both sides:

2x = ln 13 /ln 11 - 1

We'll divide by 2:

x = (ln 13 /ln 11 - 1)/2

x = (ln 13 - ln 11)/2*ln 11

x = ln (13/11)/ln 11^2

We'll compute the ratio ln (13/11)/ln 11^2:

ln (13/11) = 0.1670

ln 121 = 4.7957

x = ln (13/11)/ln 11^2 = 0.0348

The solution of the equation is: x = 0.0348.