Write the expression as a sum, difference, or product of logarithms. Assume tha

arneguet9k

arneguet9k

Answered question

2021-11-11

Write the expression as a sum, difference, or product of logarithms. Assume that all variables represent positive real numbers:
logb(m5p9n3b7)

Answer & Explanation

Melinda Olson

Melinda Olson

Beginner2021-11-12Added 20 answers

Step 1
Consider the provided logarithm expression,
logb(m5p9n3b7)
Step 2
The formula for logarithm is shown below,
logb(mn)=logbm+logbn
logb(mn)=logbmlogbn
logb(m)n=logbm
log=1
Step 3
Now, using the above formula to rewrite the above logarithm expression as,
logb(m5p9n3b7)=logb(m5p9)log(n3b7)  [Difference Rule]
=logb(m5p9)logb(n3b7)
=[logb(m5)+logb(p9)][logb(n3)+logb(b7)]  [Product Rule]
=logb(m5)+logb(p9)log(n3)logb(b7)
=5logbm+9logbp3logbn7log  [logb(m)n=nlogbm]
=5logbm+9logbp3logbn7
Step 4
Answer: The provided logarithm expression can be written as sum, difference, or product of logarithms is,
logb(m5p9n3b7)=5logbm+9logbp3logbn7

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