Question
I7 \( b^{x}=5 \) calculate \( \cdot \frac{18}{2^{-x}} \)
Ask by Perkins Hart. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[ \frac{18}{2^{-x}} = 90 \]
Solution
It looks like you're working with the equation:
\[ b^{x} = 5 \]
and you want to calculate:
\[ \frac{18}{2^{-x}} \]
Assuming \( b = 2 \), let's proceed step by step.
### Given:
\[ 2^{x} = 5 \]
### Calculate:
\[ \frac{18}{2^{-x}} \]
### Step 1: Simplify the Denominator
\[ 2^{-x} = \frac{1}{2^{x}} \]
So,
\[ \frac{18}{2^{-x}} = 18 \times 2^{x} \]
### Step 2: Substitute \( 2^{x} \) with 5
From the given equation:
\[ 2^{x} = 5 \]
Therefore,
\[ 18 \times 2^{x} = 18 \times 5 = 90 \]
### Final Answer:
\[ \frac{18}{2^{-x}} = 90 \]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve for the expression \( \frac{18}{2^{-x}} \), first, recognize that \( 2^{-x} = \frac{1}{2^x} \), so we can rewrite the expression as \( 18 \cdot 2^x \). From the equation \( b^{x} = 5 \), you want to express \( x \) in terms of \( b \) or vice versa, but it seems we don't have a specific value for \( b \). Assuming \( b \) is something like 2, we can derive \( 2^x = 5 \). Thus our expression becomes: \[ 18 \cdot 2^x = 18 \cdot 5 = 90. \] So, \( \frac{18}{2^{-x}} = 90 \) when \( b = 2 \). If \( b \) is different, the final answer will vary accordingly!
