Respuesta :
Answer:
3^x-8=8 then x=log_3(16)
3^(x-8)=8 then log_3(8)+8
Step-by-step explanation:
So if it is 3^x-8=8
then 3^x=16
and then convert to logarithmic form you write it as log_3(16)=x
_3 means the subscript (the base) is 3
So if it is 3^(x-8)=8
then the log form is log_3(8)=x-8
add 8 on both sides log_3(8)+8=x
The value of x that satisfies the given equation is 9.8929
Logarithmic equation
From the question, we are to solve [tex]3^{x-8} =8[/tex] for x, using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]
From the given equation,
[tex]3^{x-8} =8[/tex]
Take [tex]log_3[/tex] of both sides,
That is,
[tex]\log _{3} 3^{x-8} = \log _{3} 8[/tex]
This becomes,
[tex](x-8)\log _{3} 3= \log _{3} 8[/tex]
Since [tex]\log _{x} x =1[/tex],
∴ [tex]\log _{3} 3 =1[/tex]
[tex](x-8)(1)= \log _{3} 8[/tex]
[tex]x-8= \log _{3} 8[/tex]
Using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]
[tex]\log _{3} 8=\frac{\log 8}{\log 3}[/tex]
Then,
[tex]x-8=\frac{\log 8}{\log 3}[/tex]
[tex]x-8=\frac{0.9031}{0.4771}[/tex]
x - 8 = 1.8929
x = 8 + 1.8929
x = 9.8929
Hence, the value of x that satisfies the given equation is 9.8929
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