Question

If (625)x =15625,find xif 625 ^ x is equal to 15602 V find x square and x cube ​

Answer 1

Step-by-step explanation:

GIVEN

${(625)}^{x} = 15625$

${5}^{4x} = {5}^{6}$

$4x = 6$

$x = \frac{3}{2}$

then x^2 and x^3

${x}^{2} = ({ \frac{3}{2}) }^{2} = \frac{9}{4}$

$x {}^{3} = { (\frac{3}{2}) }^{3} = \frac{27}{8}$

Answer 2

The value of $\dfrac{9}{4}\text{ and }\dfrac{81}{8}.$

Explanation:

Given : $(625)^x=15625$    ................(1)

Since , $625 = 5\times5\times5\times5= 5^4$

$15625=5\times5\times5\times5\times5\times5=5^6$

Then equation (1) will become,

$(5^4)^x=5^6\\\\\Rightarrow\ 5^{4x}=5^6\\\\\Rightarrow\ 4x=6\\\\\Rightarrow\ x=\dfrac{6}{4}=\dfrac{3}{2}$

Then, $x^2=(\dfrac{3}{2})^2=\dfrac{9}{4}$

$x^3=(\dfrac{3}{2})^3=\dfrac{81}{8}$

Hence , the value of $\dfrac{9}{4}\text{ and }\dfrac{81}{8}.$

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If (625^x) = 25/(5^x), Find x

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