Question

Solve 2^x=3. round to the nearest ten thousandth

Answer 1

`2^(x) = 3`

`log_(2)3 = x`

`(log_3)/(log_2) = x`

`x = 1.585`

Answer 2

The solution of the expression is x=1.584.

Explanation:

Given : Expression
`2^x=3`

To find : Solve the expression round to the nearest ten thousandth?

Solution :

Step 1 - Write the expression,

`2^x=3`

Step 2 - Taking log both side,

`\log (2^x)=\log (3)`

Step 3 - Apply logarithmic property,
`\log a^x=x\log a`

`x\log (2)=\log (3)`

Step 4 - Solve,

`x=(\log (3))/(\log (2))`

`x=(0.477)/(0.301)`

`x=1.584`

Therefore, The solution of the expression is x=1.584.