Question

If a^x=b,b^y=c,xyz=1,what is the value of c^z?
PLSS ANSWER FAST

Answer 1

Solution :

a^x = b ---( 1 )

xyz = 1 ---( 2 )

and

b^y = c

=> (a^x)^y = c

[ from ( 1 ) ]

=> a^xy = c

=> a^xyz = c^z

=> a¹ = c^z

[ from ( 2 ) ]

Therefore ,

c^z = a

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Answer 2

$\underline{\mathfrak{\huge{The\:Question:}}}$

If $\tt{a^{x} = b , b^{z} = c , xyz = 1}$, what is the value of $\tt{c^{z}}$ ?

$\underline{\mathfrak{\huge{Your\:Answer}}}$

$\sf{Given:}$

■ $\tt{a^{x}}$ = b [Let this be equation (1)]

■ $\tt{b^{y}}$ = c [Let this be equation (2)]

■ xyz = 1 [Let this be equation (3)]

Well! To arrive at the answer, we will first start with the equation (2). We will solve it, and we will put the value of b, as the value in the equation (1). This can be written in the algebraic form like :

$\tt{(a^{x})^{y} = b^{y} = c}$

$\tt{a^{xy} = c}$ [Let this be equation (4)]

Now, from the equation (3), we can find out the value of xy :

$\tt{xyz = 1}$

$\tt{xy = \frac{1}{z}}$

Now, we can put the value of xy in equation (4) and then solve the rest :

$\tt{a^{\frac{1}{z}} = c}$

Now, take the power to the right hand side and during that, you just need to convert the power from fraction to its reciprocal :

$\tt{a = c^{\frac{z}{1}}}$

This makes the power :

$\tt{a = c^{z}}$

There's your answer !