Question

Solve The Upper Questions​

Answer 1

Answer:

are these questions fron simple equation chapter

Answer 2

(i) $6^{x-2} = 1$

We can turn any exponential number to 1 by applying this law ⇒ $a^{0}=1$

So our equation now would be $x-2=0$

Let's solve your equation step-by-step.

$x-2=0$

Step 1: Add 2 to both sides of the equation.

$x-2+2=0+2$

$x=2$

$\bf \therefore x=2 \ in \ the \ equation => 6^{x-2}=1$

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(ii) $2^{2x+2}=4^{2}$

We need to first simplify 4² into it's lowest form.

$2^{2x+2}=(2^{2})^{2}$

Now we must apply this law ⇒ $(a^{m})^{n} = a^{m\times n}$

$2^{2x+2}=2^{2\times 2 }$

$2^{2x+2}=2^{4 }$

Since the bases are the same we will solve the exponents. Our equation to find 'x' would be ⇒ $2x+2=4$

Let's solve your equation step-by-step.

$2x+2=4$

Step 1: Subtract 2 from both sides of the equation.

$2x+2-2=4-2$

$2x=2$

Step 2: Divide 2 from both sided of the equation.

$\frac{2x}{2} =\frac{2}{2}$

$x=1$

$\bf \therefore x=1 \ in \ the \ equation => 2^{2x+2}=4^{2}$

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(iii) $5^{2x+1}\div 25 = 125$

We need to first simplify 25 and 125 into it's lowest form.

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

We'll keep this law of exponent in mind for now ⇒ $a^{m}\div a^{n} = a^{m-n}$

Since the bases are the same we will solve the exponents. Our equation to find 'x' would be ⇒ $(2x+1)-2=3$

Let's solve your equation step-by-step.

$(2x+1)-2=3$

Step 1: Add 2 to both sides of the equation.

$(2x+1)-2+2=3+2$

$2x+1=5$

Step 2: Subtract 1 from both sides of the equation.

$2x+1-1=5-1$

$2x=4$

Step 3: Divide 2 from both sides of the equation.

$\frac{2x}{2}=\frac{4}{2}$

$x=2$

$\bf \therefore x=2 \ in \ the \ equation => 5^{2x+1}\div 25 = 125$

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(iv) $(\frac{5}{3})^{-4}\times (\frac{5}{3} )^{-5}=(\frac{5}{3}) ^{3x}$

We'll keep this law of exponent in mind for now ⇒ $a^{m}\times a^{n} = a^{m+n}$

Since the bases are the same we will solve the exponents. Our equation to find 'x' would be ⇒ $-4+-5=3x$

Let's solve your equation step-by-step.

$-4+-5=3x$

Step 1: Simplify both sides of the equation.

$-4-5=3x$

$-4+-5=3x$

Combine Like Terms

$(-4+-5)=3x$

$-9=3x$

Step 2: Flip the equation.

$3x=-9$

Step 3: Divide both sides by 3.

$\frac{3x}{3}=\frac{-9}{3}$

$x=-3$

$\bf \therefore x=-3 \ in \ the \ equation => \ (\frac{5}{3})^{-4}\times (\frac{5}{3} )^{-5}=(\frac{5}{3}) ^{3x}$

$\rule{300}{1}$