Question

Explain how to solve 5^(x− 2) = 8 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

$\sf\longrightarrow 5^{x -2}= 8$

Take log on both sides with base as " 10" . We have ,

$\sf\longrightarrow log_{10} 5^{x-2}= log_{10}\ 8$

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

$\sf\longrightarrow ( x -2) log_{10} 5 = log_{10} 8$

Simplify ,

$\sf\longrightarrow ( x -2 ) log_{10}5 = log_{10} 2^3$

Again simplify using the property of log ,

$\sf\longrightarrow (x-2) log 5 = 3 log 2$

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

$\sf\longrightarrow ( x - 2 ) = \dfrac{ 3\times 0.301}{0.69}$

Simplify the RHS ,

$\sf\longrightarrow x - 2 = 1.30$

Add 2 both sides ,

$\sf\longrightarrow \boxed{\blue{\sf x = 3.30}}$

Hence the Value of x is 3.30 .

Answer 2

Answer:

Step-by-step explanation:

log 5^(x - 2) = log(8)

(x - 2)log(5) = log(8)

Log(5)=0.69897

log(8) = 0.80309

x - 2  = log(8) / log(5)

x - 2 = 1.29203

x = 2 + 1.29203

x = 3.29203