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Montano1993 [528]
3 years ago
8

Use the following steps to prove that log b(xy)- log bx+ log by.

Mathematics
1 answer:
borishaifa [10]3 years ago
3 0

Answer with Step-by-step explanation:

a.x=b^p

y=b^q

Taking both sides log

log x=plog b

Using identity:logx^y=ylogx

p=\frac{logx}{log b}=log_b x

Using identity:log_x y=\frac{log y}{log x}

log y=qlog b

q=\frac{log y}{log b}=log_b y

b.xy=b^pb^q

We know that

x^a\cdot x^b=x^{a+b}

Using identity

xy=b^{p+q}

c.log_b(xy)=log_b(b^{p+q})

log_b(xy)=(p+q)log_b b

Substitute the values then we get

log_b(xy)=(log_b x+log_b y)

By using log_b b=1

Hence, log_b(xy)=log_b x+log_b y

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