Using logarithm to calculate the following leaving your answer correct to two significant figures log 3 to the power x is equal to log 5
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Apply the power rule of logarithms.
The equation is given as $\log 3^x = \log 5$.
Using the logarithm property $\log a^b = b \log a$, we can rewrite the left side:
$$ x \log 3 = \log 5 $$
Step 2: Isolate $x$.
To find $x$, divide both sides by $\log 3$:
$$ x = \frac{\log 5}{\log 3} $$
Step 3: Calculate the numerical value of $x$.
Using a calculator for base-10 logarithms:
$$ \log 5 \approx 0.69897 $$
$$ \log 3 \approx 0.47712 $$
Now, substitute these values into the equation for $x$:
$$ x = \frac{0.69897}{0.47712} $$
$$ x \approx 1.46497 $$
Step 4: Round the answer to two significant figures.
The first significant figure is 1, and the second is 4. The digit following the second significant figure is 6, which is 5 or greater, so we round up the second significant figure.
$$ x \approx 1.5 $$
The value of $x$ correct to two significant figures is $\boxed{1.5}$.
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