Question 895·Easy·Math

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The function $h$ is defined by $h(x)=5^{x-1}$ . For which value of $x$ is $h(x)=125$ ?

In an exponential equation, the unknown input sits in the exponent. When a function’s output is given, set its rule equal to that output; a Desmos regression can then find the input. Define the function first, and use $x_1$ and $\sim$ to solve. The exponent you recognize from a familiar power may not be the input the question asks for.

Hints

Hint 1
The notation $h(x)$ means the output produced by input $x$ . You’re given the output and asked for the input. What equation do you get when you replace $h(x)$ with its rule?
Hint 2
A regression finds a number that makes an equation true. After defining $h$ in Desmos, enter $h(x_1)\sim125$ . Desmos will find $x_1$ , the input that produces the given output.

Step-by-step

Solve for the input with Desmos
Step 1
Turn the given output into an equation
The problem gives $h(x)=125$ , so the output is $125$ . Replace $h(x)$ with its given rule to find the input that produces it: $5^{x-1}=125$ .
Step 2
Find the input in Desmos
Type $h(x)=5^{x-1}$ , then $h(x_1)\sim125$ . The $\sim$ tells Desmos to find a value of $x_1$ that gives the specified output. Under PARAMETERS, it shows $x_1=4$ . That’s the input the question asks for, so $x=4$ . Choice C.

Question 895·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this