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Use the following steps to prove that log(xy)= logbx+ logby.a. Let x bP and y = b. Solve these expressions for p and q, respectively.b. Use the property b*bV = b**"y to express xy in terms of b, p, and q.c. Compute log (xy) and simplify.+ba. Let x bP and y b. Solve these expressions for p and q, respectively.q =(Simplify your answers.)

Question
Use the following steps to prove that log(xy)= logbx+ logby.
a. Let x bP and y = b. Solve these expressions for p and q, respectively.
b. Use the property b*bV = b**"y to express xy in terms of b, p, and q.
c. Compute log (xy) and simplify.
+
b
a. Let x bP and y b. Solve these expressions for p and q, respectively.
q =
(Simplify your answers.)
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Use the following steps to prove that log(xy)= logbx+ logby. a. Let x bP and y = b. Solve these expressions for p and q, respectively. b. Use the property b*bV = b**"y to express xy in terms of b, p, and q. c. Compute log (xy) and simplify. + b a. Let x bP and y b. Solve these expressions for p and q, respectively. q = (Simplify your answers.)

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Step 1

We take log base b on both sides of x=b^p. 

p=log_b (x)

x=b"
Or, log,Xlog,(b")
Or, og,plog,b
=
Or, og,p
Or, logx p
Or, p logx
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x=b" Or, log,Xlog,(b") Or, og,plog,b = Or, og,p Or, logx p Or, p logx

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Step 2

We take log base b on both sides of y=b^q.

Answer(a): p=log base b (x)

q=log base b (y)

y=b
Or, logby log (b°)
Or, logy log,b
Or, logyq1
Or, log,y q
Or, qlogy
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y=b Or, logby log (b°) Or, logy log,b Or, logyq1 Or, log,y q Or, qlogy

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Step 3

We know x=b^p and y=b^q. 

So, xy=b^(p...

ху%3БР.БЯ
Or, ху-bp+9
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ху%3БР.БЯ Or, ху-bp+9

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Math

Calculus

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