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

`x=e^3`

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)=(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`