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Solve for x, rounding to the nearest hundredth. 10^(x)=68 Answer:

Solve for x x , rounding to the nearest hundredth.\newline10x=68 10^{x}=68 \newlineAnswer:

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Full solution

Q. Solve for x x , rounding to the nearest hundredth.\newline10x=68 10^{x}=68 \newlineAnswer:
  1. Write Equation to Solve: Write down the equation that needs to be solved.\newlineWe have the equation 10x=6810^{x} = 68.\newlineWe need to solve for xx.
  2. Apply Logarithm: Apply the logarithm to both sides of the equation to solve for xx. Taking the logarithm base 1010 of both sides, we get log⁡(10x)=log⁡(68)\log(10^{x}) = \log(68).
  3. Simplify Using Logarithm Property: Simplify the equation using the property of logarithms that log⁡(ab)=blog⁡(a)\log(a^b) = b\log(a). This gives us xlog⁡(10)=log⁡(68)x\log(10) = \log(68). Since log⁡(10)\log(10) is 11, the equation simplifies to x=log⁡(68)x = \log(68).
  4. Calculate Log Value: Calculate the value of log⁡(68)\log(68) using a calculator.x=log⁡(68)≈1.83250891270624x = \log(68) \approx 1.83250891270624
  5. Round to Nearest Hundredth: Round the value of xx to the nearest hundredth.x≈1.83x \approx 1.83

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