Question

Q.1) Find the value of xif log2 (x + 6 =2
a)2
b)3
c)
4
d)-1​

Answer 1

Hey There

Here's The Answer

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• Refer to the Attachment

Hope It Helps

Answer 2

Given :

$\sf log_{2}(x + 6) = 2$

To find :

• The value of x.

Solution :

$\sf \implies log_{2}(x + 6) = 2$

Now , we know that :-

$\sf if \: \: \: { {\sf log_{a}(b) = t } } \\ \sf \: then \: b = {a}^{t}$

Therefore :-

$\sf \implies x + 6 = {2}^{2}$

$\sf \implies x + 6 = 4$

$\sf \implies x = 4 - 6$

$\sf \implies x = - 2$

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Verification of Answer :-

Put x =-2 in :-

$\: \: \sf log_{2}(x + 6) = 2$

If we get RHS and LHS equal then our answer is correct.

RHS = 2

LHS =>

$\implies\sf log_{2}( - 2 + 6)$

$\implies\sf log_{2}( 4)$

$\implies\sf log_{2} ({2})^{2}$

We know that :-

$\boxed{ \sf log_{e} {(a)}^{b} =b \times log_{e} {(a)}}$

$\implies\sf2 \ \times log_{2} ({2})$

$\implies\sf 2 \times 1 = 2$

Therefore , RHS = LHS

hence verified.

So our answer is correct.