Question

question⤵⤵

if 4x =8³ then the value of x is

(a)3/2 (b)9/2 (C)3 (d)9​

Answer 1

Answer:

Option(c) 3 is the required value of x

Step-by-step explanation:

Explanation:

$4^x$ = $8^3$

According to the question we need to find out the value of x.

$(a^m)^n = a^{mn}$  is the power rule for exponents. Multiply the exponent by the power to raise a number with an exponent to that power.

Step 1:

We have, $4 ^ x= 8^3$

This can be written as, $(2^2)^{x} = (2^3)^2$

As we know the power of exponent rule, $(a^m)^n$ = $a^{mn}$

Where 4 can be written as 2 × 2

and 8 can be written as 2 × 2 × 2

Now, on comparing both sides we get,

⇒ 2x = 6

⇒ x = $\frac{6}{2}$ = 3

Final answer:

Hence,3 is the required value of x.

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Answer 2

The value of $x$  in $4^{x}$ is b) 9/2.

Power of Power Rules of Exponents:

The power of a power rule in exponents is used to simplify the algebraic statement when a base is raised to a power followed by the raising of the full equation to another power.

i.e.     $(n^{x})^{y} = n^{xy}$

Given Equation:  $4^{x} = 8^{3}$ ;

Applying The power of power rule On the Left Hand Side,we get

$4^{x} = (2^{2} )^{x}\\= 2^{2x}$

Similarly, On the Right Hand Side,we get

$8^{3} = (2^{3})^{3}\\= 2^{9}$

Now, on comparing both sides we get

$2^{2x} = 2^{9}\\(Since\ the\ Base\ is\ Same,\ we\ can\ compare\ Exponentially\ too)\\\Rightarrow 2x = 9\\\Rightarrow x = \frac{9}{2}$

Therefore, the value of  $" x "\ is\ \frac{9}{2}$.

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