Question

if 5√5 X 625 X 4√5 = 5 ^n+1/5 what will be the value of n?

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Answer 1

Answer:

The value of n is 6.8613.

Step-by-step explanation:

Step : 1 Making anything simple makes everything easier. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies.

Step : 2  Exponents are used to show this when continuously multiplying a number by itself. can be used, for example, to represent 7 x 7 x 7. In this instance, the exponent is "3," which indicates how many times the number 7 has been multiplied. In this case, the base—the number that is really being multiplied—is 7. Simply said, exponents and powers show how many times a number may be multiplied.

Step : 3 $5 \sqrt{5} \times 625 \times 4 \sqrt{5}=5^n+\frac{1}{5}$

Switch sides

$5^n+\frac{1}{5}=5 \sqrt{5} \times 625 \times 4 \sqrt{5}$

Simplify

$12500(\sqrt{5})^2-\frac{1}{5}: \quad 62500-\frac{1}{5}$

$5^n=62500-\frac{1}{5}$

Apply exponent rules

$\mathrm{n} \ln (5)=\ln \left(62500-\frac{1}{5}\right)n \ln (5)=\ln \left(62500-\frac{1}{5}\right): \quad n=\frac{\ln \left(\frac{312499}{5}\right)}{\ln (5)}$

Solve

$n=\frac{\ln \left(\frac{312499}{5}\right)}{\ln (5)}$

n=6.8613

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Answer 2

The value of n is 6.862

• A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

• The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfil the equality are known as the equation's solutions.
• Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

Here, according to the given information, we are given that,

$5\sqrt{5} .(625).(4\sqrt{5} )=5^{n} +\frac{1}{5} .$

Then, we get,

$12500.(5) = 5^{n} +\frac{1}{5} .$

Or, $62500-\frac{1}{5} =5^{n} .$

Or, $62499.8 = 5^{n}$

Now, taking log on both sides, we get,

$4.796 = nlog5$

Or, $n = 6.862$

Hence, the value of n is 6.862.

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