Question

if x=(100)^a, y=(10000)^b and z=(10)^c, express log (10*√y)/x²*z³) in terms of a,b,c.

Answer 1

please mark it as brainlist, if it is correct.
as logx=2a, logy=4b, logz=c

Answer 2

Answer:

$\log\frac{(10\times \sqrt y)}{x^2z^3}=1+2b-4a-3c$

Step-by-step explanation:

Given : If $x=(100)^a,\ y=(10000)^b,\ z=(10)^c$

To find : Express $\log\frac{(10\times \sqrt y)}{x^2z^3}$ in terms of a,b,c?

Solution :

$x=(100)^a$

$x=(10^2)^a$

$x=(10)^{2a}$

Taking log both side,

$\log x=2a$ ....(1)

$y=(10000)^b$

$y=(10)^{4b}$

Taking log both side,

$\log y=4b$ .....(2)

$z=(10)^{c}$

Taking log both side,

$\log z=c$ .....(3)

Now, We expand the expression

$\log\frac{(10\times \sqrt y)}{x^2z^3}=\log 10+\log\sqrt y-\log x^2-\log z^3$

$\log\frac{(10\times \sqrt y)}{x^2z^3}=1+\frac{1}{2}\log y-2\log x-3\log z$

Using (1), (2) and (3),

$\log\frac{(10\times \sqrt y)}{x^2z^3}=1+\frac{1}{2}(4b)-2(2a)-3(c)$

$\log\frac{(10\times \sqrt y)}{x^2z^3}=1+2b-4a-3c$

Therefore, $\log\frac{(10\times \sqrt y)}{x^2z^3}=1+2b-4a-3c$