Respuesta :

Answer:

see explanation

Step-by-step explanation:

Using the rule of logarithms

log[tex]x^{n}[/tex] = nlogx

Given

a = [tex]b^{x}[/tex] ← take the log of both sides

loga = log[tex]b^{x}[/tex] = xlogb ⇒ x = [tex]\frac{loga}{logb}[/tex]

b = [tex]c^{y}[/tex] ← take the log of both sides

logb = log[tex]c^{y}[/tex] = ylogc ⇒ y = [tex]\frac{logb}{logc}[/tex]

c = [tex]a^{z}[/tex] ← take the log of both sides

logc = log[tex]a^{z}[/tex] = zloga ⇒ z = [tex]\frac{logc}{loga}[/tex]

Thus

xyz = [tex]\frac{loga}{logb}[/tex] × [tex]\frac{logb}{logc}[/tex] × [tex]\frac{logc}{loga}[/tex] ← cancel loga, logb, logc on numerators/denominators

Hence xyz = 1

samuelnwobi9

Answer: xyz = 1

Step-by-step explanation:

a = b^x given

introducing log into both sides

log a = log b^x

log a = x log b

divide both sides by log b

x = log a/ log b ... (1)

b = c^y given

introducing log into both sides

log b = log c^y

log b = y log c

divide both sides by log c

y = log b/ log c ... (2)

c = a^z given

introducing log to both sides

log c = log a^z

log c = z log a

divide both sides by log a

z = log c / log a ... (3)

Multiplying equations 1, 2 and 3 together;

x*y *z = (log a/ log b) * (log b/ log c)

* ( log c/ log a)

Therefore,

xyz = 1. proved

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