Question

Using the properties of exponents and logarithms, find the value of x in 19 + 2 ln x = 25.

Answer 1

$19+2\ln x=25\ \ \ |-19\\\\2\ln x=6\ \ \ |:2\\\\\ln x=3\iff x=e^3$

$\text{Used de.finition of the logarithm:}\ \ \ \log_ab=c\iff a^c=b$

Answer 2

Answer:

$x=e^3$

Step-by-step explanation:

• The first step is to pass 19 to subtract the other side

$2\cdot ln(x)=25-19$

$2\cdot ln(x)=6$

• The second step is to pass the 2 to divide the other side

$ln(x)=\frac{6}{2}$

$ln(x)=3$

• The final step is take into account the general form of logarithmic expression.

$ln(a)=b$    ------->     $e^b=a$

According to the the previous, if we have $ln(x)=3$, the value of x would be:

$e^3=x$

$x=e^3$