Solve for x, rounding to the nearest hundredth. 29*10^((x)/(5))=203 Answer:

Isolate variable x: First, we need to isolate the term with the variable x. To do this, we divide both sides of the equation by 29. \[ \frac{29 \cdot 10^{(x/5)}}{29} = \frac{203}{29} \]Calculate right side: After dividing both sides by 29, we get: \[ 10^{(x/5)} = \frac{203}{29} \] Now we can calculate the right side of the equation. \[ 10^{(x/5)} \approx 7.00 \]Take natural logarithm: Next, we need to solve for x. To do this, we take the natural logarithm (ln) of both sides of the equation to remove the exponent on the left side. \[ \ln(10^{(x/5)}) = \ln(7.00) \]Simplify left side: Using the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$, we can simplify the left side of the equation: \[ \frac{x}{5} \cdot \ln(10) = \ln(7.00) \]Solve for x: Now we can solve for x by multiplying both sides of the equation by 5 and then dividing by $\ln(10)$: \[ x = \frac{5 \cdot \ln(7.00)}{\ln(10)} \]Calculate x value: Finally, we calculate the value of x using a calculator: \[ x \approx \frac{5 \cdot \ln(7.00)}{\ln(10)} \approx \frac{5 \cdot 1.94591}{2.30259} \approx 4.23 \]

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Solve for
x, rounding to the nearest hundredth.

29*10^((x)/(5))=203
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $29 \cdot 10^{\frac{x}{5}}=203$ $\newline$ Answer:

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Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

29 \cdot 10^{\frac{x}{5}}=203

\newline

Answer:

Isolate variable x: First, we need to isolate the term with the variable x. To do this, we divide both sides of the equation by $29$ . $\newline$ $\frac{29 \cdot 10^{(x/5)}}{29} = \frac{203}{29}$
Calculate right side: After dividing both sides by $29$ , we get: $\newline$ $10^{(x/5)} = \frac{203}{29}$ $\newline$ Now we can calculate the right side of the equation. $\newline$ $10^{(x/5)} \approx 7.00$
Take natural logarithm: Next, we need to solve for x. To do this, we take the natural logarithm (ln) of both sides of the equation to remove the exponent on the left side. $\newline$ $\ln(10^{(x/5)}) = \ln(7.00)$
Simplify left side: Using the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$ , we can simplify the left side of the equation: $\newline$ $\frac{x}{5} \cdot \ln(10) = \ln(7.00)$
Solve for x: Now we can solve for x by multiplying both sides of the equation by $5$ and then dividing by $\ln(10)$ : $\newline$ $x = \frac{5 \cdot \ln(7.00)}{\ln(10)}$
Calculate x value: Finally, we calculate the value of x using a calculator: $\newline$ $x \approx \frac{5 \cdot \ln(7.00)}{\ln(10)} \approx \frac{5 \cdot 1.94591}{2.30259} \approx 4.23$