How do you find the inverse of ${log}_{1.25} (x) = y$ $log _ 1.25 (x)=y$ ?

Question

1951 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-05T08:37:57

See below

By definition of logarithm ${log}_{1.25} x = y \Leftrightarrow y^{1.25} = x$ $log_1.25x=y hArr y^(1.25)=x$

But we know that $1.25 = \frac{5}{4}$ $1.25=5/4$

$y^{\frac{5}{4}} = x$ $y^(5/4)=x$ powering both sides to 4 we have

$(y^(5/cancel4))^cancel4=x^4$

$y^5=x^4$ stracting 5th root

$root(5)(y^5)=y=root(5)(x^4)=x^(4/5)$

How do you find the inverse of log _ 1.25 (x)=ylog1.25(x)=ylog _ 1.25 (x)=y?