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We are given the values of $lg3$ and $lg5$, and we are asked to find the value of $lg15$.

ArithmeticLogarithmsLogarithm PropertiesArithmetic Operations
2025/4/28

1. Problem Description

We are given the values of lg3lg3 and lg5lg5, and we are asked to find the value of lg15lg15.

2. Solution Steps

We know that 15=3×515 = 3 \times 5.
Using the properties of logarithms, we have:
lg(ab)=lg(a)+lg(b)lg(ab) = lg(a) + lg(b)
Therefore,
lg15=lg(3×5)=lg3+lg5lg15 = lg(3 \times 5) = lg3 + lg5
We are given lg3=0.4771lg3 = 0.4771 and lg5=0.6990lg5 = 0.6990.
lg15=0.4771+0.6990=1.1761lg15 = 0.4771 + 0.6990 = 1.1761

3. Final Answer

lg15=1.1761lg15 = 1.1761

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