Question

Need answer for 6 and 7 question ASAP will give brainlist to who answered

Answer 1

Answer:

6.  x = 2

7.  35721

Step-by-step explanation:

Question 6

Given equation:

$8^{-4} \times 8^7=8^{2x-1}$

$\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:$

$\implies 8^{-4+7}=8^{2x-1}$

$\implies 8^{3}=8^{2x-1}$

$\textsf{Apply the exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):$

$\implies 3=2x-1$

Add 1 to both sides:

$\implies 3+1=2x-1+1$

$\implies 4=2x$

Divide both sides by 2:

$\implies \dfrac{4}{2}=\dfrac{2x}{2}$

$\implies 2=x$

Therefore, x = 2.

Question 7

Given identity:

$\sf (a-b)^2=a^2-2ab+b^2$

To find the square of 189, rewrite 189 as (200 - 11).

Therefore, a = 200 and b = 11.

Substitute these values into the given identity and solve:

$\begin{aligned}\sf (a-b)^2 & =\sf a^2-2ab+b^2\\\implies \sf 189^2 = (200-11)^2 & =\sf 200^2-2(200)(11)+11^2\\& = \sf 40000 - 400(11)+121\\& = \sf 40000-4400+121\\& = \sf 35600+ 121\\& = \sf 35721 \end{aligned}$