Isolate term with exponent: Isolate the term with the exponent. To solve for b, we need to isolate the term 8^b. We can do this by dividing both sides of the equation by 4. 4 * 8^b = 53 (4 * 8^b) / 4 = 53 / 4 8^b = 53 / 4 8^b = 13.25Take logarithm of both sides: Take the logarithm of both sides. To solve for the exponent b, we can take the logarithm of both sides of the equation. We can use any logarithm, but it's most convenient to use the logarithm with base 8, which is log base 8, or the natural logarithm (ln) and then convert it. Let's use the natural logarithm: ln(8^b) = ln(13.25)Apply power rule of logarithms: Apply the power rule of logarithms. The power rule of logarithms states that ln(a^x) = x * ln(a). We can apply this rule to the left side of the equation. b * ln(8) = ln(13.25)Solve for b: Solve for b. To solve for b, we divide both sides of the equation by ln(8). b = ln(13.25) / ln(8) Now we can use a calculator to find the values of ln(13.25) and ln(8). b ≈ 1.2837 / 2.0794 b ≈ 0.617

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$4 \cdot 8^{b} = 53$ $\newline$ Find the value of `b`

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Grade 6

Multiply whole numbers

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4 \cdot 8^{b} = 53

\newline

Find the value of `b`

Isolate term with exponent: Isolate the term with the exponent. $\newline$ To solve for $b$ , we need to isolate the term $8^b$ . We can do this by dividing both sides of the equation by $4$ . $\newline$ $4 \times 8^b = 53$ $\newline$ $(4 \times 8^b) / 4 = 53 / 4$ $\newline$ $8^b = 53 / 4$ $\newline$ $8^b = 13.25$
Take logarithm of both sides: Take the logarithm of both sides. $\newline$ To solve for the exponent $b$ , we can take the logarithm of both sides of the equation. We can use any logarithm, but it's most convenient to use the logarithm with base $8$ , which is log base $8$ , or the natural logarithm (ln) and then convert it. $\newline$ Let's use the natural logarithm: $\newline$ $\ln(8^b) = \ln(13.25)$
Apply power rule of logarithms: Apply the power rule of logarithms. $\newline$ The power rule of logarithms states that $\ln(a^x) = x \cdot \ln(a)$ . We can apply this rule to the left side of the equation. $\newline$ $b \cdot \ln(8) = \ln(13.25)$
Solve for b: Solve for b. $\newline$ To solve for b, we divide both sides of the equation by $\ln(8)$ . $\newline$ $b = \frac{\ln(13.25)}{\ln(8)}$ $\newline$ Now we can use a calculator to find the values of $\ln(13.25)$ and $\ln(8)$ . $\newline$ $b \approx \frac{1.2837}{2.0794}$ $\newline$ $b \approx 0.617$