MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Property 1

Expand log ...

Question

Expand ${log}_{a} \sqrt[3]{x^{7} y^{8} \div \sqrt[4]{z}}$

Open in App

Solution

Consider $l o g_{a} \sqrt[3]{x^{7} y^{8} \div \sqrt[4]{z}}$

$l o g_{a} \sqrt[3]{x^{7} y^{8} \div \sqrt[4]{z}} = l o g_{a} (\sqrt[3]{\frac{x^{7} y^{8}}{\sqrt[4]{z}}})$

$= l o g_{a} {(\frac{x^{7} y^{8}}{\sqrt[4]{z}})}^{\frac{1}{3}}$

$= \frac{1}{3} l o g_{a} (\frac{x^{7} y^{8}}{\sqrt[4]{z}})$

$= \frac{1}{3} {l o g_{a} (x^{7} y^{8}) - l o g_{a} (\sqrt[4]{z})}$

$= \frac{1}{3} ⎧ ⎪ ⎨ ⎪ ⎩ l o g_{a} (x^{7} y^{8}) - l o g_{a} (z)^{\frac{1}{4}} ⎫ ⎪ ⎬ ⎪ ⎭$

$= \frac{1}{3} {l o g_{a} (x^{7} y^{8}) - \frac{1}{4} l o g_{a} (z)}$

$= \frac{1}{3} {l o g_{a} (x^{7}) + l o g_{a} (y^{8}) - \frac{1}{4} l o g_{a} (z)}$

$l o g_{a} \sqrt[3]{x^{7} y^{8} \div \sqrt[4]{z}}$ $= \frac{1}{3} {7 l o g_{a} (x) + 8 l o g_{a} (y) - \frac{1}{4} l o g_{a} (z)}$

Suggest Corrections

thumbs-up

1

Similar questions

\frac{x}{8} - \frac{y}{7} = \frac{17}{28}; \frac{x}{7} - \frac{y}{8} = 1

Q. Consider the addition of numbers with different bases,

(X)_{7} + (Y)_{8} + (W)_{10} + (Z) = (K)_{9}

If X = 36, Y = 67, W = 98 and K = 241 then, Z is equal to

{log}_{a} 2 = x

{log}_{a} 3 = y

{log}_{a} 5 = z

. Find the value in each of the following in terms of

x

y

z

{log}_{a} 15

{log}_{a} 8

{log}_{a} 30

{log}_{a} (\frac{27}{125})

{log}_{a} (3 \frac{1}{3})

{log}_{a} 1.5

\frac{x}{3} + \frac{y}{4} = 4, \frac{5 x}{6} - \frac{y}{8} = 4

\sqrt[3]{y} (2 \sqrt[3]{y} - \sqrt[3]{y^{8}})

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Laws of Logarithm with Use

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon