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:
Option 4 - x=6.292
Step-by-step explanation:
Given : Expression [tex]4^{x-5}=6[/tex]
To find : Solve the expression using change of base formula?
Solution :
Expression [tex]4^{x-5}=6[/tex]
Change of base formula is [tex]\log_b y=\frac{\log_a y}{\log_a b}[/tex]
Step 1 - Taking log both side in the expression,
[tex]\log(4^{x-5})=\log (6)[/tex]
Apply logarithmic property, [tex]\log a^x=x\log a[/tex]
[tex](x-5)\log(4)=\log (6)[/tex]
Step 2 - Taking log one side,
[tex]x-5=\frac{\log (6)}{\log(4)}[/tex]
Step 3 - Apply change base formula,
[tex]x-5=\log_4 6[/tex]
Step 4 - Solve,
[tex]x=\log_4 6+5[/tex]
[tex]x=1.292+5[/tex]
[tex]x=6.292[/tex]
Therefore, Option 4 is correct.
