Answer

Verified

337.5k+ views

**Hint:**In the given question, we have been asked to find the value of ‘x’ and it is given that\[{{\left( 125 \right)}^{x}}=625\]. In order to solve the question, first we write the numbers in exponential form. Then we need to use the property of product of power which states that if there is a power to the power, then we multiply the power such that\[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}\]. After that we will equate the powers with each other and solve in a way we solve the general equation.

**Formula used:**

The property of product of power which states that if there is a power to the power, then we multiply the power such that\[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}\].

**Complete step by step solution:**

We have given that,

\[\Rightarrow {{\left( 125 \right)}^{x}}=625\]

As we know that,

\[\Rightarrow 5\times 5\times 5={{5}^{3}}=125\] And

\[\Rightarrow 5\times 5\times 5\times 5={{5}^{4}}=625\]

Substituting \[125={{5}^{3}}\] and \[625={{5}^{4}}\] in the given equation, we get

\[\Rightarrow {{\left( {{5}^{3}} \right)}^{x}}={{5}^{4}}\]

Using the property of product of a power, i.e.

If there is a power to the power, then we multiply the power.

\[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}\]

Applying the property in the equation, we get

\[\Rightarrow {{5}^{3x}}={{5}^{4}}\]

Now both the sides base are equal i.e. 5.

Equation powers with each other, we get

\[\Rightarrow 3x=4\]

Now solving for the value of ‘x’.

Dividing both the sides of the equation by 3, we get

\[\Rightarrow \dfrac{3x}{3}=\dfrac{4}{3}\]

Simplifying the above, we get

\[\Rightarrow x=\dfrac{4}{3}\]

**Therefore, the value of \[x=\dfrac{4}{3}\] is the required answer.**

**Note:**While solving these types of questions, students need to remember the properties of exponent and powers. For converting the number into exponential form, we will need to find the prime factorization of that number and we will get our number in exponential form. Exponents are used to write the same number in multiplication form using a simple format.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Which places in India experience sunrise first and class 9 social science CBSE

The list which includes subjects of national importance class 10 social science CBSE

What is pollution? How many types of pollution? Define it

State the laws of reflection of light