Expand each logarithm. log₄5 x
1 answer:
If the expression is log₄5 x,then the expansion of this will look like
(log 5+ log x)/log 4.
Given that the expression is log₄5 x.
We are required to find the expansion of the expression.
Base change theorem says that =
. We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.
The expression is log₄5 x.
log₄5 x=(log 5+log x)/log 4
(We know that = log b/ log a and log mn =log m +log n)
Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.
Learn more about base change theorem at brainly.com/question/14998693
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Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is D) x = 4. Hope this helps and have a great day!
Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is D) x = 4. Hope this helps and have a great day!