Express the constant 3 as a logarithm with base 10. Recall that x means _10 x.
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Morning Jerome — let's get this done.
Step 1: Express the constant $3$ as a logarithm with base $10$. Recall that $\lg x$ means $\log_{10} x$.
$$ 3 = 3 \times 1 = 3 \times \log_{10} 10 = \log_{10} (10^3) = \log_{10} 1000 $$
Step 2: Apply the power rule of logarithms, $c \log_b M = \log_b (M^c)$, to the term $2 \lg 5$.
$$ 2 \lg 5 = \lg (5^2) = \lg 25 $$
Step 3: Substitute these simplified terms back into the original expression.
$$ \lg 1000 - \lg 2 - \lg 25 $$
Step 4: Apply the quotient rule of logarithms, $\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)$, from left to right.
First, combine the first two terms:
$$ \lg 1000 - \lg 2 = \lg \left(\frac{1000}{2}\right) = \lg 500 $$
Step 5: Combine the result with the third term.
$$ \lg 500 - \lg 25 = \lg \left(\frac{500}{25}\right) $$
Step 6: Simplify the fraction inside the logarithm.
$$ \lg 20 $$
The simplified expression is:
$$ \boxed{\lg 20} $$
Last free one today — make it count tomorrow, or type /upgrade for unlimited.
