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

Answer:

x = -1.59

Step-by-step 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 ,

$\sf\longrightarrow x = \dfrac{ ln7}{ln 4 } - \dfrac{ 3ln4}{ln4}$

Simplify ,

$\sf\longrightarrow x = \dfrac{ ln4 }{ln7 } -3$

On simplifying , we will get ,

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