Math, asked by hhhhhhhhhh, 1 year ago

If x^a=c^b and x^c=c^a then prove that a^2=bc

Answers

Answered by Anonymous

You have log(x)=(b/a)log(c) and log(x)=(a/c)log(c) From these b/a=a/c Hence, a^2=bc

Anonymous: I don't think logarithms are required here, anyway this is the answer.

hhhhhhhhhh: Please hwlp without log

Anonymous: Raise the power of first equation to 1/a and that of second to 1/c then you have x=c^(b/a)=c^(a/c)

Anonymous: Raise the power of first equation to 1/a and that of second to 1/c then you have x=c^(b/a)=c^(a/c) Equate the powers since the bases are same. Then you shall have a^2=BC

hhhhhhhhhh: Thanks

Answered by TPS

$x^{a}= c^{b} \\ x= ( c^{b} )^{ \frac{1}{a} } \\ x=c^{ \frac{b}{a} }$

$x^{c}= c^{a} \\ x=(c^{a})^{ \frac{1}{c} } \\ x= c^{ \frac{a}{c} }$

thus
$c^{ \frac{b}{a} }=c^{ \frac{a}{c} } \\ \frac{b}{a} = \frac{a}{c} \\ a^{2}=bc$

hhhhhhhhhh: Thank you so much

Previous Question

Next Question