Properties of Logarithms score 100%
1. write the expression as a single logarithm
b) log_b(q2t8)
2. write the expression as a single logarithm
d) none of these
3. expand the logarithmic expression
b) log_5 7+5log_5a
4. use change of base formula to evaluate log_2 74
c) 6.209
5. a construction explosion has an intensity I of 1.25 x 10–4 W/m2. Find the loudness of the sound in decibels if W/m2. round to the nearest tenth.
a) 81 decibels
Logarithmic function convert into the expression as a single logarithm to simplify the function.
Single logarithm function is the function in which the log of the function appears only single time. The number of logarithmic terms convert into the single logarithm function by using the logarithmic operations.
Given information-
The first logarithmic function given in the problem is,
[tex]2\log_bq + 8 \log_bt[/tex]
Let the expression of above function in a single logarithm is [tex]f(x)[/tex]. Thus,
[tex]f(x)=2\log_bq + 8 \log_bt[/tex]
The power rule of logarithmic function says, that the coefficient of log function is raised to its power.
[tex]f(x)=\log_bq^2 + \log_bt^2[/tex]
For the same base of logarithmic function, the log can be added by multiplying their argument. thus,
[tex]f(x)=\log_b(q^2 t^8)[/tex]
Hence the expression as a single logarithm for the problem 1 is [tex]\log_b(q^2 t^8)[/tex].
The second logarithmic function given in the problem is,
[tex]4\log x - 6 \log (x+2)[/tex]
Let the expression of above function in a single logarithm is [tex]f(x)[/tex]. Thus,
[tex]f(x)=4\log x - 6 \log (x+2)[/tex]
The power rule of logarithmic function says, that the coefficient of log function is raised to its power.
[tex]f(x)=\log x^4 - \log (x+2)^6[/tex]
For the same base of logarithmic function, the log can be added by multiplying their argument. thus,
[tex]f(x)=\log(x^4 (x+2)^6)[/tex]
Hence the expression as a single logarithm for the problem 2 is [tex]\log(x^4 (x+2)^6)[/tex].
Thus,
Learn more about the rules of logarithmic function here;
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