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Question : 12 of 86

Marks: +1, -0

Given that

10^{0.48}=x, 10^{0.70}=y

x^{z}=y^{2} .

then the value of

z

is close to:

1.45
1.88
2.9
3.7

Solution:

Concept:

Use laws of indices to equate powers after expressing both sides with base 10.

Explanation:

Given

x = 10^{0.48}

and

y = 10^{0.70}

.

Then

x^z = (10^{0.48})^z = 10^{0.48z}

.

Also

y^2 = (10^{0.70})^2 = 10^{1.40}

.

The equation

x^z = y^2

becomes

10^{0.48z} = 10^{1.40}

.

Since bases are equal, equate exponents:

0.48z = 1.40

.

Thus

z = \frac{1.40}{0.48} = \frac{140}{48} = \frac{35}{12} \approx 2.9167

.

The value is close to 2.9.

Answer:

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