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# If x = 10^1.4, y = 10^0.7, and x^z = y^3, then what is the value of z

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Math Expert
Joined: 02 Sep 2009
Posts: 58312
If x = 10^1.4, y = 10^0.7, and x^z = y^3, then what is the value of z  [#permalink]

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10 Apr 2019, 01:08
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Difficulty:

15% (low)

Question Stats:

76% (01:15) correct 24% (01:00) wrong based on 33 sessions

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If $$x = 10^{1.4}$$, $$y = 10^{0.7}$$, and $$x^z = y^3$$, then what is the value of z ?

(A) 0.5
(B) 0.66
(C) 1.5
(D) 2
(E) 3

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Re: If x = 10^1.4, y = 10^0.7, and x^z = y^3, then what is the value of z  [#permalink]

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10 Apr 2019, 02:39
Bunuel wrote:
If $$x = 10^{1.4}$$, $$y = 10^{0.7}$$, and $$x^z = y^3$$, then what is the value of z ?

(A) 0.5
(B) 0.66
(C) 1.5
(D) 2
(E) 3

$$(10^{1.4z}=10^{0.7*3}$$
$$z=2.1/1.4=1.5$$
imo, option c.
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Re: If x = 10^1.4, y = 10^0.7, and x^z = y^3, then what is the value of z  [#permalink]

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10 Apr 2019, 11:43
$$x=10^1.4$$, $$y=10^0.7$$ $$y=10^0.7$$, and $$x^z=y^3$$
thus 1.4z =$$0.7*3$$= 2.1

hence z = 3/2 = 1.5
Re: If x = 10^1.4, y = 10^0.7, and x^z = y^3, then what is the value of z   [#permalink] 10 Apr 2019, 11:43
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