solve (√6)^8x = 216^x - 3. (1 point) x = -9 x = -3 x = 0 x = 4 6. (05.01) if $240 is invested at an interest…

Explanation:

Step1: Rewrite bases

Rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ and $216$ as $6^{3}$. So the equation $(\sqrt{6})^{8x}=216^{x - 3}$ becomes $(6^{\frac{1}{2}})^{8x}=(6^{3})^{x - 3}$.

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^{m})^{n}=a^{mn}$. We have $6^{\frac{1}{2}\times8x}=6^{3\times(x - 3)}$, which simplifies to $6^{4x}=6^{3x-9}$.

Step3: Set exponents equal

Since the bases are the same, we can set the exponents equal: $4x=3x - 9$.

Step4: Solve for x

Subtract $3x$ from both sides: $4x-3x=3x - 9-3x$, so $x=-9$.

Answer:

$x=-9$

Explanation for second part:

Step1: Identify values for compound - interest formula

We are given that $P = 240$ (principal amount), $r=0.09$ (annual interest rate, since $9%=0.09$), $n = 12$ (compounded monthly), and $t = 14$ (number of years).

Step2: Substitute values into formula

The compound - interest formula is $A=P(1+\frac{r}{n})^{nt}$. Substitute the values: $A = 240(1+\frac{0.09}{12})^{12\times14}$.

Step3: Calculate inside the parentheses first

$\frac{0.09}{12}=0.0075$, then $1+\frac{0.09}{12}=1 + 0.0075=1.0075$.

Step4: Calculate the exponent

$nt=12\times14 = 168$.

Step5: Calculate the power

$(1.0075)^{168}\approx2.8495$.

Step6: Calculate A

$A=240\times2.8495 = 683.88$.

Answer:

There seems to be an error in the provided options as the correct value is approximately $$683.88$. For the first part, the answer is $x=-9$.