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Solve each equation. Ro

log_(2)(v-9)+3.3=5.6

Solve each equation. Ro $\newline$ $1$ ) $\log _{2}(v-9)+3.3=5.6$

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Convert between exponential and logarithmic form: all bases

Full solution

Q. Solve each equation. Ro

\newline

1

)

\log _{2}(v-9)+3.3=5.6

Subtract to isolate logarithmic expression: Subtract $3.3$ from both sides to isolate the logarithmic expression. $\newline$ $\log_{2}(v-9) = 5.6 - 3.3$ $\newline$ $\log_{2}(v-9) = 2.3$
Convert to exponential form: Convert the logarithmic equation to exponential form to solve for $v$ . $2^{2.3} = v - 9$
Calculate using calculator: Calculate $2^{2.3}$ using a calculator. $\newline$ $2^{2.3} \approx 4.924$ $\newline$ $v - 9 \approx 4.924$
Add to solve for $v$ : Add $9$ to both sides to solve for $v$ . $\newline$ $v \approx 4.924 + 9$ $\newline$ $v \approx 13.924$

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