Respuesta :
The approximate value of q in the logarithmic equation is 0.585.
The given logarithmic equation is [tex]\rm q+log_2(6)=2q+2[/tex]
It is required to find the value of 'q'.
What is Logarithm?
It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b=c\\\rm log_ac=b[/tex]
We have a logarithmic equation:
[tex]\rm q+log_2(6)=2q+2[/tex]
After simplification the above equation we get;
[tex]\rm q+log_2(6)=2q+2\\\rm q-2q=-log_2(6)+2\\\rm -q=-log_2(6)+2\\[/tex].....(1)
From the logarithmic table, we get the value of [tex]\rm log_2(6)[/tex]
[tex]\rm log_2(6)=2.5849[/tex]
Putting this value in equation (1), we get:
[tex]\rm -q=-log_2(6)+2\\\rm -q=-2.5849+2\\\rm -q=-0.5849\\\rm q=0.5849 \approx 0.585\\[/tex]
Thus, the approximate value of q in the logarithmic equation is 0.585.
Learn more about the Logarithm here:
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