Respuesta :
Answer:
[tex]4^x-5=6[/tex] gives the solution [tex]x=\frac{\log(11)}{\log(4)}[/tex].
[tex]4^{x-5}=6[/tex] gives the solution [tex]x=\frac{\log(6)}{\log(4)}+5[/tex].
Step-by-step explanation:
I will solve both interpretations.
If we assume the equation is [tex]4^{x}-5=6[/tex], then the following is the process:
[tex]4^x-5=6[/tex]
Add 5 on both sides:
[tex]4^x=6+5[/tex]
Simplify:
[tex]4^x=11[/tex]
Now write an equivalent logarithm form:
[tex]\log_4(11)=x[/tex]
[tex]x=\log_4(11)[/tex]
Now using the change of base:
[tex]x=\frac{\log(11)}{\log(4)}[/tex].
If we assume the equation is [tex]4^{x-5}=6[/tex], then we use the following process:
[tex]4^{x-5}=6[/tex]
Write an equivalent logarithm form:
[tex]\log_4(6)=x-5[/tex]
[tex]x-5=\log_4(6)[/tex]
Add 5 on both sides:
[tex]x=\log_4(6)+5[/tex]
Use change of base formula:
[tex]x=\frac{\log(6)}{\log(4)}+5[/tex]
Answer:
6.292
Step-by-step explanation:
I got it right on the test.
