Evaluate 10(1,000,000), Simplify 3(a) − (b) + 2(c), and Calculate the future value of an investment.

Question

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Here are the solutions to the problems:

5. Evaluate: $\log_{10}(1,000,000)$

Understand the definition of a logarithm.
The expression $\log_{10}(1,000,000)$ asks "to what power must 10 be raised to get 1,000,000?".
Express 1,000,000 as a power of 10.
$1,000,000 = 10^6$
Substitute this back into the logarithm.
$\log_{10}(10^6) = 6$
The correct option is B.
$\boxed{\text{B. } 6}$
6. Simplify: $3\log(a) - \log(b) + 2\log(c)$
Apply the power rule of logarithms, $n\log(x) = \log(x^n)$ .
$3\log(a) = \log(a^3)$ $2\log(c) = \log(c^2)$
Substitute these back into the expression.
$\log(a^3) - \log(b) + \log(c^2)$
Apply the quotient rule of logarithms, $\log(x) - \log(y) = \log\left(\frac{x}{y}\right)$ .
$\log\left(\frac{a^3}{b}\right) + \log(c^2)$
Apply the product rule of logarithms, $\log(x) + \log(y) = \log(xy)$ .
$\log\left(\frac{a^3}{b} \cdot c^2\right) = \log\left(\frac{a^3 c^2}{b}\right)$
The correct option is A.
$\boxed{\text{A. } \log\left(\frac{a^3 c^2}{b}\right)}$
9. A savings account grows by 8% each year. If the initial amount is 1000, what will it be after 2 years?
Identify the initial amount, rate, and time.
Initial amount $P = 1000$
Annual growth rate $r = 8\% = 0.08$
Number of years $t = 2$
Use the compound interest formula $A = P(1 + r)^t$ .
$A = 1000(1 + 0.08)^2$
Calculate the value inside the parenthesis.
$A = 1000(1.08)^2$
Calculate $(1.08)^2$ .
$A = 1000(1.1664)$
Multiply to find the final amount.
$A = 1166.4$
The correct option is B.
$\boxed{\text{B. } 1166.4}$

Evaluate 10(1,000,000), Simplify 3(a) - (b) + 2(c), and Calculate the future value of an investment.