Question

if (9^4)^2 = 3^x then value of x is

Answer 1

Answer:

answer must be in these option

14

16

15

17

l have given a hint you must try to do it yourself too

Step-by-step explanation:

btw the answer is 16

Answer 2

Answer:

The value of x is 32.

Step-by-step explanation:

Given,

$( {9}^{4} )^{4} = {3}^{x}$

We want to find value of x.

We know,

$9 = {3}^{2} = 3 \times 3$

So,

$( {9}^{4} )^{4} = {3}^{x} \\ (( {3}^{2}) ^{4})^{4} = {3}^{x} \\ {( {3}^{2 \times 4}) }^{4} = {3}^{x} \\( {3}^{8}) ^{4} = {3}^{x} \\ {3}^{8 \times 4} = {3}^{x} \\ {3}^{32} = {3}^{x} \\ x = 32$

Here applied formulas are ${x}^{ {a}^{b} } = {x}^{a \times b}$

and ${x}^{a} = {x}^{b} \: then \: a = b$

This is a problem of Power of indices.

Some important formulas of Power of indices:

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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