How Do You Solve 10log1019 in Logarithms?

• m0286
In summary, the conversation discusses how to evaluate the logarithm 10log1019 when there is a number in front of the log. The participant suggests using a property of logarithms to simplify the calculation, but others mention that it is not necessary and suggest simply multiplying the result of the log by ten. They also mention that there is a table of rules for the log function and that the base 10 logarithm is tabulated, so there is no need to change the base.
m0286
Hello sorry to post another so soon. This book is VERY hard to learn from... its not very good at explaining. The question says:
Evaluate the following logarithm: 10log1019. It never showed me how to do it when there's a number in front of the log. What I got from the log 1019 is log19/log10=1.27875. Now do I multiply this by 10 since that's the number infront.. I have no clue!

THNX AGAIN!

Yes, there's also a property of logarithms that applies here, there's probably a table of rules for the log function, this property will be there, it should be the only one with a coefficient infront of the function.

The ten out front has nothing to do with the log. The ten just multiplies the result of the log. You can, if you choose, apply a property of the logarithm which permits you to "absorb" the coefficient in front of the log into the log's argument, but there's absolutely no reason to do so in this case. (This property is what whozum is talking about.)

$$a \log_b x = \log_b x^a$$

Once again, there's no reason to invoke this property unless you want to. I would suggest just multiplying the result of the logarithm by ten.

- Warren

I was merely pointing out that possibility. Perhaps he had seen it before and it would help him compute the log without the coefficient, although the answers are the same.

Incidentally,$\log_{10}$ also written $\lg$ is tabulated (or a specific function on a smart pocket calculator),so there's no need to change th basis.

Daniel.

1. What is a logarithm?

A logarithm is a mathematical function that represents the power to which a base number must be raised to produce a given number. It is the inverse function of exponentiation.

2. How do I evaluate a logarithm?

To evaluate a logarithm, you can rewrite it in exponential form and then solve for the exponent. For example, in the expression 10log10 19, the base is 10, so you can rewrite it as 10^x = 19. Using basic algebra, you can solve for x, which in this case would be 1.924.

3. What is the value of log10 1?

The value of log10 1 is 0, since any number raised to the power 0 equals 1. In general, the logarithm of 1 to any base is always 0.

4. Can a logarithm be negative?

Yes, a logarithm can be negative. This can occur when the base is greater than 1 and the argument (the number inside the logarithm) is between 0 and 1. For example, log10 0.5 is approximately -0.301.

5. What are some practical applications of logarithms?

Logarithms are commonly used in various fields such as science, engineering, finance, and statistics. They are useful for representing very large or small numbers, and for converting between different units of measurement. They are also used in exponential growth and decay models, and in calculating the pH level of a substance.

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