Question

find X if 5 to the power of 2x+1 divide by 25=125

Answer 1

Required Answer:-

Given:

• $\rm \dfrac{ {5}^{2x + 1} }{25} = 125$

To find:

• The value of x.

Solution:

We have,

$\rm \implies \dfrac{ {5}^{2x + 1} }{25} = 125$

$\rm \implies \dfrac{ {5}^{2x + 1} }{25} \times 25= 125 \times 25$

$\rm \implies {5}^{2x + 1} = 125 \times 25$

$\rm \implies {5}^{2x + 1} = {5}^{3} \times {5}^{2}$

$\rm \implies {5}^{2x + 1} = {5}^{3 + 2}$

$\rm \implies {5}^{2x + 1} = {5}^{5}$

Comparing base, we get,

$\rm \implies 2x + 1 = 5$

$\rm \implies 2x = 5 - 1$

$\rm \implies 2x = 4$

$\rm \implies x = 2$

★ Hence, the value of x is 2.

Answer:

• The value of x is 2.

Important Formula For Solving Indices Questions:

• $\rm {x}^{a} \times {x}^{b} = {x}^{a + b}$
• $\rm ({x}^{a})^{b} = {x}^{ab}$
• $\rm \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$
• $\rm {x}^{0} = 1 \: \: \: \: (x \neq 0)$
• $\rm {x}^{a} = {x}^{b} \implies a = b \: \: \: (x \neq 1)$

Answer 2

Answer:

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