Question

Solve 4x − 5 = 6 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

Answer:

Step-by-step explanation:

4^x-5 = 6

Apply the ln rule

x^y = z

(y)*ln(x) = z

4^x-5 = 6

(x-5)*ln(4) = ln(6)

x-5 = ln(6)/ln(4)

x-5 = 1.292

x = 6.292

Therefore, the correct answer is the last option.

!!

Answer 2

Answer:

Option 4 - x=6.292  

Step-by-step explanation:

Given : Expression $4^{x-5}=6$

To find : Solve the expression using change of base formula?

Solution :

Expression $4^{x-5}=6$

Change of base formula is $\log_b y=\frac{\log_a y}{\log_a b}$

Step 1 - Taking log both side in the expression,

$\log(4^{x-5})=\log (6)$

Apply logarithmic property, $\log a^x=x\log a$

$(x-5)\log(4)=\log (6)$

Step 2 - Taking log one side,

$x-5=\frac{\log (6)}{\log(4)}$

Step 3 - Apply change base formula,

$x-5=\log_4 6$

Step 4 - Solve,

$x=\log_4 6+5$

$x=1.292+5$

$x=6.292$

Therefore, Option 4 is correct.