Question

if a^x =b ,b^y = c ,c^z = a then xyz is??

Answer 1

$\underline {\underline {\text{\large{Solution : }}}} \\ \\ \underline{ \text{PROCESS - 1}} \\ \\ \text{Given that,} \\ { \text{a}}^{ \text{x}} = \text{b}, \: \: \: { \text{b}}^{ \text{y}} = \text{c} \: \: \text{and} \: \: \: { \text{c}}^{ \text{z}} = \text{a} \\ \\ \text{Multiplying the terms, we get -} \\ { \text{a}}^{ \text{x}} \times { \text{b}}^{ \text{y}} \times { \text{c}}^{ \text{z}} = \text{a} \times \text{b} \times \text{c} \\ \\ \text{Comparing the like powers of a, b and c, we get -} \\ \text{x = 1, y = 1 and z = 1} \\ \\ \therefore \boxed{\text{xyz} = 1}\\ \\ \underline{ \text{PROCESS - 2}} \\ \\ \text{Given that} \\ { \text{a}}^{ \text{x}} = \text{b} \implies \text{x loga = logb}\\ { \text{b}}^{ \text{y}} = \text{c} \implies \text{y logb = logc} \\ { \text{c}}^{ \text{z}} = \text{a} \implies \text{z logc = loga} \\ \\ \text{On multiplication, we get -} \\ \text{(xyz)(loga logb logc) = (loga logb logc)} \\ \\ \to \boxed{\text{xyz = 1}} \: \: \: \{ \: \because \text{loga logb logc } \neq 0 \: \}$

$\maltese \underline {\text{\large{MarkAsBrainliest}}}\maltese$

Answer 2

Hey mate !

Given that,

${a}^{x} = b \\ {b}^{y} = c \\ {c}^{z} = a$

We have

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

Now, open the brackets.

${b}^{xyz} = {b}^{1}$

Equating powers, we get

$\boxed{xyz = 1}$