Solve for y if 1-9 2y-1-00811-3-243 - 1-3 2y-5-27y-1-10000

(3^ 2)^2y 1.(3^4 . 10^ 4)^1/3/3^5/2 = 3^ (2y 5).3^3 ( y 1/3 )/10^4/3 ⇒3^ 4y+2+4/3 5/2/10^4/3=3^ 2y+5+y 1/10^4/3 ⇒ 3^ 4y+5/6=3^ y+4 Equating with same bases: ⇒ ...

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Byju's Answer

Standard X

Mathematics

Exponents

Solve for y i...

Question

Solve for y if
$\frac{{(\frac{1}{9})}^{2 y - 1} (.0081)^{\frac{1}{3}}}{\sqrt{243}} = {(\frac{1}{3})}^{2 y - 5} \sqrt[3]{\frac{27^{y - 1}}{10000}}$

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Solution

$\frac{(3^{- 2})^{2 y - 1} . (3^{4} . 10^{- 4})^{\frac{1}{3}}}{3^{\frac{5}{2}}}$ = $\frac{3^{- (2 y - 5)} {.3}^{3 (\frac{y - 1}{3})}}{10^{\frac{4}{3}}}$
$\Rightarrow \frac{3^{- 4 y + 2 + \frac{4}{3} - \frac{5}{2}}}{10^{\frac{4}{3}}} = \frac{3^{- 2 y + 5 + y - 1}}{10^{\frac{4}{3}}}$
$\Rightarrow 3^{- 4 y + \frac{5}{6}} = 3^{- y + 4}$
Equating with same bases:
$\Rightarrow - 4 y + \frac{5}{6} = - y + 4$
$\Rightarrow y = \frac{- 19}{18}$

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Solve for y if (19)2y−1(.0081)13√243=(13)2y−53√27y−110000

(3−2)2y−1.(34.10−4)13352 = 3−(2y−5).33(y−13)1043 ⇒3−4y+2+43−521043=3−2y+5+y−11043 ⇒3−4y+56=3−y+4 Equating with same bases: ⇒−4y+56=−y+4 ⇒y=−1918

Solve for y if
$\frac{{(\frac{1}{9})}^{2 y - 1} (.0081)^{\frac{1}{3}}}{\sqrt{243}} = {(\frac{1}{3})}^{2 y - 5} \sqrt[3]{\frac{27^{y - 1}}{10000}}$