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$((a)/(3),oo) [a,oo) Question 7 2pts Find the value of log_(b)((x^(2)z)/(sqrty)) given that: {:[log_(b)(x)=7.8],[log_(b)(y)=6.6],[log_(b)(z)=8.7]:} Round to two decimal places. ◻ Question 8 2 pts Write an equivalent exponential form of$

$\left(\frac{a}{3}, \infty\right)$ $\newline$ $[a, \infty)$ $\newline$ Question $7$ $\newline$ $2 \mathrm{pts}$ $\newline$ Find the value of $\log _{b}\left(\frac{x^{2} z}{\sqrt{y}}\right)$ given that: $\newline$ $\begin{array}{l} \log _{b}(x)=7.8 \\ \log _{b}(y)=6.6 \\ \log _{b}(z)=8.7 \end{array}$ $\newline$ Round to two decimal places. $\newline$ $\square$ $\newline$ Question $8$ $\newline$ $2$ pts $\newline$ Write an equivalent exponential form of

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Math Problems

Algebra 2

Identify properties of logarithms

Full solution

\left(\frac{a}{3}, \infty\right)

\newline

[a, \infty)

\newline

Question

7

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2 \mathrm{pts}

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Find the value of

\log _{b}\left(\frac{x^{2} z}{\sqrt{y}}\right)

given that:

\newline

\begin{array}{l} \log _{b}(x)=7.8 \\ \log _{b}(y)=6.6 \\ \log _{b}(z)=8.7 \end{array}

\newline

Round to two decimal places.

\newline

\square

\newline

Question

8

\newline

2

pts

\newline

Write an equivalent exponential form of

Break down expression: Use the properties of logarithms to break down the expression $\log_b\left(\frac{x^2z}{\sqrt{y}}\right)$ into separate logarithms. $\newline$ $\log_b\left(\frac{x^2z}{\sqrt{y}}\right) = \log_b(x^2) + \log_b(z) - \log_b(\sqrt{y})$
Apply power property: Apply the power property of logarithms to $\log_b(x^2)$ and $\log_b(\sqrt{y})$ . $\newline$ $\log_b(x^2) = 2 \cdot \log_b(x)$ $\newline$ $\log_b(\sqrt{y}) = \left(\frac{1}{2}\right) \cdot \log_b(y)$
Substitute given values: Substitute the given values into the expression. $\newline$ $2 \cdot \log_b(x) + \log_b(z) - \frac{1}{2} \cdot \log_b(y) = 2 \cdot 7.8 + 8.7 - \frac{1}{2} \cdot 6.6$
Perform calculations: Perform the calculations. $\newline$ $2 \times 7.8 + 8.7 - \left(\frac{1}{2}\right) \times 6.6 = 15.6 + 8.7 - 3.3$
Add and subtract values: Add and subtract the values to get the final result. $\newline$ $15.6 + 8.7 - 3.3 = 24.3 - 3.3 = 21.0$