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Logarithms Practice Test 2

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Question : 9 of 39

Marks: +1, -0

If

a^x = b

b^y = c

c^z = a

, then value of

xyz

is:

0
1
2
3

Solution:

Concept:

Use substitution and exponent laws to compare powers with the same base.

Explanation:

Given

a^x=b

,

b^y=c

,

c^z=a

.

Substitute

b=a^x

into

b^y=c

:

c=(a^x)^y=a^{xy}

.

Now use

c^z=a

:

(a^{xy})^z=a

.

So

a^{xyz}=a^1

.

Comparing exponents gives

xyz=1

.

Answer:

xyz=1

, so option B is correct.

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