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< Previous Bookwork code: 4G Work out the value of r in the equality below. 0.0058=5.8times 10^r (1) Watch video Calculator not allowed Answ ier

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< Previous Bookwork code: 4G Work out the value of r in the equality below. 0.0058=5.8times 10^r (1) Watch video Calculator not allowed Answ ier

< Previous Bookwork code: 4G Work out the value of r in the equality below. 0.0058=5.8times 10^r (1) Watch video Calculator not allowed Answ ier

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MiloElite · Tutor for 8 years

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<p> -3</p>

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<p> The question asks us to find the value of \( r \) in the equation \( 0.0058 = 5.8 \times 10^{r} \).<br /><br />Step 1: Understand the Equation<br />The equation \( 0.0058 = 5.8 \times 10^{r} \) is an exponential equation where we need to find the value of the exponent \( r \).<br /><br />Step 2: Isolate the Exponential Term<br />The exponential term \( 10^{r} \) is already isolated on one side of the equation.<br /><br />Step 3: Solve for \( r \)<br />To find \( r \), we can divide both sides of the equation by 5.8:<br />\[<br />\frac{0.0058}{5.8} = 10^{r}<br />\]<br />\[<br />10^{-3} = 10^{r}<br />\]<br />Since the bases are the same, we can equate the exponents:<br />\[<br />-3 = r<br />\]<br /><br />Step 4: Verify the Solution<br />Substituting \( r = -3 \) back into the original equation \( 0.0058 = 5.8 \times 10^{r} \), we get:<br />\[<br />0.0058 = 5.8 \times 10^{-3}<br />\]<br />\[<br />0.0058 = 0.0058<br />\]<br />The equation holds true, confirming that \( r = -3 \) is the correct solution.<br /><br />Therefore, the value of \( r \) is -3.</p>
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