Question

if (5/3)_5×(5/3)11=(5/3)8x,then x=?​

Answer 1

Answer:

ANSWER

it may be two ways

Step-by-step explanation:

WAY 1

(5/3)5*(5/3)11=(5/3)8x

》(5/3*5/1)*(5/3*11/1)=(5/3*8x/1)

》25/3*55/3=40x/3

》270/4

WAY 2

(5/3)^5*(5/3)^11=(5/3)^8x

》5+11=8x

》16=8x

》16/8=x

》2=x

thank you

Answer 2

The value of x = 3/4

Given :

$\displaystyle \sf{ {\bigg( \frac{5}{3} \bigg) }^{ - 5} \times {\bigg( \frac{5}{3} \bigg) }^{ 11} = {\bigg( \frac{5}{3} \bigg) }^{ 8x} }$

To find :

The value of x

Formula :

We are aware of the formula on indices that

$\sf \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\displaystyle \sf{ {\bigg( \frac{5}{3} \bigg) }^{ - 5} \times {\bigg( \frac{5}{3} \bigg) }^{ 11} = {\bigg( \frac{5}{3} \bigg) }^{ 8x} }$

Step 2 of 2 :

Find the value of x

We use the formula

$\boxed{ \sf \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} \: \: }$

Thus we have

$\displaystyle \sf{ {\bigg( \frac{5}{3} \bigg) }^{ - 5} \times {\bigg( \frac{5}{3} \bigg) }^{ 11} = {\bigg( \frac{5}{3} \bigg) }^{ 8x} }$

$\displaystyle \sf{ \implies {\bigg( \frac{5}{3} \bigg) }^{ - 5 + 11} = {\bigg( \frac{5}{3} \bigg) }^{ 8x} }$

$\displaystyle \sf{ \implies {\bigg( \frac{5}{3} \bigg) }^{ 6} = {\bigg( \frac{5}{3} \bigg) }^{ 8x} }$

$\displaystyle \sf{ \implies {\bigg( \frac{5}{3} \bigg) }^{ 8x} = {\bigg( \frac{5}{3} \bigg) }^{ 6} }$

$\displaystyle \sf{ \implies 8x = 6 }$

$\displaystyle \sf{ \implies x = \frac{6}{8} }$

$\displaystyle \sf{ \implies x = \frac{3}{4} }$

Hence the required value of x = 3/4

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