Question

Solve In 2 + In x= 5. Round to the nearest thousandth, if necessary.

Answer 1

The value of x nearest to thousandths is 74.207

Solution:

Given that,

`\text{ln } 2 + \text{ln } x = 5` ------ eqn 1

We can use logarithmic properties to solve for "x"

Using logarithmic properties:

`\ln (mn) = \ln m + \ln n`

Therefore, apply the above property in eqn 1

`\text{ln } 2 + \text{ln } x = 5\\\\\text{ln } 2x = 5`

By using the logarithmic property,

`\text{If } \ln x = a , \text{ then } x = e^a`

Apply the above logarithmic property in above expression

`\text{ln } 2x = 5\\\\2x = e^5`

Solve the above equation

We know that,

`e^5 = 148.413159103`

[ use calculator ]

Therefore,

`2x = 148.413159103\\\\x = (148.413159103)/(2)\\\\x = 74.2065795513\\\\x \approx 74.207`

Therefore, the value of x nearest to thousandths is 74.207