Question

Explain how to solve 4^(x+3)=7 using the change of base formula log_by=log y/ log b. Round to the nearest thousandth

Answer 1

x = -1.59

Explanation:

We are here given a equation and we need to solve out for x. The given equation is ,

`\sf\longrightarrow 4^(( x +3))= 7`

Take log to the base " e " on both sides , so that we can remove the variable from the exponent .

`\sf\longrightarrow log_e 4^(x+3)= log_e 7`

Simplify using the property of log ,
`\sf log a^m = m log a` , we have ,

`\sf\longrightarrow (x + 3) ln 4 = ln 7`

Distribute by opening the brackets ,

`\sf\longrightarrow x ln 4 + 3 ln 4 = ln 7`

This can be written as ,

`\sf\longrightarrow x ln 4 = ln 7 - 3ln4`

Divide both sides by ln 4 ,

`\sf\longrightarrow x = ( ln7)/(ln 4 ) - ( 3ln4)/(ln4)`

Simplify ,

`\sf\longrightarrow x = ( ln4 )/(ln7 ) -3`

On simplifying , we will get ,

`\sf\longrightarrow \boxed{\blue{\sf x = -1.59 }}`