Question

Find the value of the unknown constant . The sum is in the picture. pls solve it in a notebook . it's urgent​

Answer 1

2b - 6 + 3 = 5

2b = 8

b = 4

Answer 2

Step-by-step explanation:

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$\displaystyle{ {5}^{2b - 6} \times 125 = (\frac{1}{5}) {}^{ - 5} }$

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$\displaystyle{ \implies \: {5}^{2b - 6} \times 125 = ( \frac{1}{5}) {}^{ - 5} }$

As we know that,

$\sf{ {a}^{ - n} = \frac{1}{ {a}^{n} } }$

• 125 = 5 X 5 X 5

$\displaystyle{ \implies \: {5}^{2b - 6} \times {5}^{3} = {5}^{5} }$

As we know that,

$\sf{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

$\displaystyle{ \implies \: {5}^{(2b - 6) + 3} = {5}^{5} }$

As now the bases are same so we can now equate with the powers:

$\displaystyle{ \implies \: (2b - 6) + 3 = 5}$

$\displaystyle{ \implies \: 2b - 6 = 5 - 3} \:$

$\displaystyle{ \implies \: 2b - 6 = 2} \:$

$\displaystyle{ \implies \: 2b = 2 + 6} \:$

$\displaystyle{ \implies \: 2b = 8} \:$

$\displaystyle{ \implies \: b = \cancel\frac{8}{2} } \:$

$\displaystyle{ \implies \: b = 4} \:$

∴ Value of the unknown constant(b) is 4.

$\red{\mid{\fbox{\tt{More \: Information :}}\mid}} \:$

$\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$