Write the equation in logarithmic form.
Assume that all constants are positive and not equal to 1 .
$$
5^{n}=a
$$

HintStarting with the graph of $f(x)=9^{x}$, write the equation of the graph that results when:
(a) $f(x)$ is shifted 5 units downward. $y=$
(b) $f(x)$ is shifted 2 units to the left. $y=$
(c) $f(x)$ is reflected about the $x$-axis. $y=$

Question

Write the equation in logarithmic form.
Assume that all constants are positive and not equal to 1 .
$$
5^{n}=a
$$

HintStarting with the graph of $f(x)=9^{x}$, write the equation of the graph that results when:
(a) $f(x)$ is shifted 5 units downward. $y=$
(b) $f(x)$ is shifted 2 units to the left. $y=$
(c) $f(x)$ is reflected about the $x$-axis. $y=$

Accepted Answer

∻Solution by Steps∻ ### Question 1: Write the equation in logarithmic form for $5^n = a$. ‖ step 1 ⋮ Start with the given equation: $5^n = a$. ‖ ‖ step 2 ⋮ Apply the definition of logarithms: $\log_b(a) = c$ if and only if $b^c = a$. ‖ ‖ step 3 ⋮ Using the definition, rewrite $5^n = a$ in logarithmic form: $\log_5(a) = n$. ‖ ∻Answer∻ ⚹ $\log_5(a) = n$ ⚹ ∻Key Concept∻ ⚹Logarithmic Form⚹ ∻Explanation∻ ⚹The logarithmic form of an equation $b^c = a$ is $\log_b(a) = c$.⚹ ### Question 2: Write the equation of the graph that results when $f(x) = 9^x$ is shifted 5 units downward. ‖ step 1 ⋮ Start with the function $f(x) = 9^x$. ‖ ‖ step 2 ⋮ To shift the graph 5 units downward, subtract 5 from the function: $y = 9^x - 5$. ‖ ∻Answer∻ ⚹ $y = 9^x - 5$ ⚹ ∻Key Concept∻ ⚹Vertical Shift⚹ ∻Explanation∻ ⚹Shifting a graph downward by $k$ units involves subtracting $k$ from the function.⚹ ### Question 3: Write the equation of the graph that results when $f(x) = 9^x$ is shifted 2 units to the left. ‖ step 1 ⋮ Start with the function $f(x) = 9^x$. ‖ ‖ step 2 ⋮ To shift the graph 2 units to the left, replace $x$ with $x + 2$: $y = 9^{x + 2}$. ‖ ∻Answer∻ ⚹ $y = 9^{x + 2}$ ⚹ ∻Key Concept∻ ⚹Horizontal Shift⚹ ∻Explanation∻ ⚹Shifting a graph to the left by $k$ units involves replacing $x$ with $x + k$ in the function.⚹ ### Question 4: Write the equation of the graph that results when $f(x) = 9^x$ is reflected about the $x$-axis. ‖ step 1 ⋮ Start with the function $f(x) = 9^x$. ‖ ‖ step 2 ⋮ To reflect the graph about the $x$-axis, multiply the function by $-1$: $y = -9^x$. ‖ ∻Answer∻ ⚹ $y = -9^x$ ⚹ ∻Key Concept∻ ⚹Reflection about the $x$-Axis⚹ ∻Explanation∻ ⚹Reflecting a graph about the $x$-axis involves multiplying the function by $-1$.⚹◊What is the logarithmic form of the equation $5^{n}=a$ assuming all constants are positive and not equal to 1?⍭ Generate me a similar question◊

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