Step 1: Identify the given value and the expression to evaluate. Given: log 6.5 = 0.8129 Evaluate: 2 log 6.5 + log 650 Step 2: Substitute the given value of log 6.5 into the expression. 2 log 6.5 + log 650 = 2(0.8129) + log 650 Step 3: Simplify log 650 using the properties of logarithms. We can write 650 as 6.5 × 100. Using the logarithm property log(AB) = log A + log B: log 650 = log (6.5 × 100); log 650 = log 6.5 + log 100 Since the base of the logarithm is not specified, we assume it is base 10. Therefore, log 100 = 2 (because 10² = 100). Substitute the value of log 6.5: log 650 = 0.8129 + 2; log 650 = 2.8129 Step 4: Substitute the value of log 650 back into the expression and calculate. 2(0.8129) + 2.8129 1.6258 + 2.8129 4.4387 The final answer is 4.4387.

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Given: 6.5 = 0.8129

April 2, 2026Mathematics

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Answer

\text{4.4387}

Step-by-step solution

4 steps

Identify the given value and the expression to evaluate.
Given: $\log 6.5 = 0.8129$
Evaluate: $2 \log 6.5 + \log 650$
Substitute the given value of $\log 6.5$ into the expression.
$2 \log 6.5 + \log 650 = 2(0.8129) + \log 650$
Simplify $\log 650$ using the properties of logarithms.
We can write 650 as $6.5 \times 100$ .
Using the logarithm property $\log(AB) = \log A + \log B$ :
$\log 650 = \log (6.5 \times 100)$ $\log 650 = \log 6.5 + \log 100$
Since the base of the logarithm is not specified, we assume it is base 10.
Therefore, $\log 100 = 2$ (because $10^2 = 100$ ).
Substitute the value of $\log 6.5$ :
$\log 650 = 0.8129 + 2$ $\log 650 = 2.8129$
Substitute the value of $\log 650$ back into the expression and calculate.
$2(0.8129) + 2.8129$ $1.6258 + 2.8129$ $4.4387$

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Given: 6.5 = 0.8129

Answer

Step-by-step solution

Identify the given value and the expression to evaluate.

Substitute the given value of log⁡6.5\log 6.5log6.5 into the expression.

Simplify log⁡650\log 650log650 using the properties of logarithms.

Substitute the value of log⁡650\log 650log650 back into the expression and calculate.

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More Mathematics Questions

Substitute the given value of $\log 6.5$ into the expression.

Simplify $\log 650$ using the properties of logarithms.

Substitute the value of $\log 650$ back into the expression and calculate.