Use log5 2 0.4307 to approximate the value of log5 4.
log5</sub) 4
= log5</sub) (2^2)
= 2log5</sub) 2
= 2(0.4307)
= ...
since 4=2^2, log4 = 2*log2
To approximate the value of log5 4 using the given log5 2 value (0.4307), we need to use the property of logarithms that states:
log a (b^c) = c * log a (b)
Therefore, to find log5 4, we can rewrite it as log5 (2^2) since 4 = 2^2:
log5 4 = log5 (2^2)
Using the property mentioned earlier, we can rewrite it as:
log5 (2^2) = 2 * log5 2
Now, substitute the given value of log5 2 (0.4307) into the equation:
log5 4 ≈ 2 * (0.4307)
Calculating the approximation:
log5 4 ≈ 2 * 0.4307
log5 4 ≈ 0.8614
Therefore, the approximate value of log5 4 using the given log5 2 value is 0.8614.
To approximate the value of log5 4 using the given information (log5 2 ≈ 0.4307), we can use the properties of logarithms.
First, let's recall the logarithmic property:
log(base a) b = log(base c) b / log(base c) a
To approximate log5 4, we can use the property mentioned above with the base of 2 as follows:
log5 4 = log2 4 / log2 5
We know that log2 4 is equal to 2 since 2^2 = 4.
Now, let's calculate log2 5:
log2 5 = log5 5 / log5 2
Since log5 5 is equal to 1 (since 5^1 = 5), and we have the value of log5 2 given as 0.4307, we can substitute these values into the equation:
log5 4 ≈ 2 / 0.4307
Simplifying the expression, we get:
log5 4 ≈ 4.64
Therefore, the approximate value of log5 4 using the given information (log5 2 ≈ 0.4307) is approximately 4.64.