evaluates log 0.225base10 if log 3 base10=0.477and log5base10=0.699?
.225 = 15^2/1000
log .225 = 2log15 - 3
...
To evaluate log 0.225 base 10, we can use the properties of logarithms.
1. Begin by using the logarithm power rule:
log (a^b) = b * log a
2. Rewrite 0.225 as a power of 10:
0.225 = 10^(-0.225)
3. Using the logarithm property, rewrite the equation as:
log (10^(-0.225)) base 10
4. Use the logarithm power rule to simplify further:
log (10^(-0.225)) base 10 = -0.225 * log 10 base 10
5. Since log 10 base 10 equals 1, we have:
-0.225 * 1 = -0.225
Therefore, log 0.225 base 10 is approximately equal to -0.225.
To evaluate log 0.225 base 10, we can use the properties of logarithms.
First, let's rewrite the given equations using the property logb(x) = y as an equation of the form x = b^y:
log 3 base 10 = 0.477 --> 3 = 10^0.477
log 5 base 10 = 0.699 --> 5 = 10^0.699
Now, let's focus on log 0.225 base 10. We can rewrite it as an equation:
log 0.225 base 10 = y --> 0.225 = 10^y
To find the value of y, we need to solve this equation for y. Taking the logarithm (base 10) of both sides, we have:
log 0.225 base 10 = log(10^y) base 10
Using the property logb(x^y) = y * logb(x), we can simplify the right side:
log 0.225 base 10 = y * log 10 base 10
Since log 10 base 10 equals 1, we can further simplify:
log 0.225 base 10 = y
Therefore, y = log 0.225 base 10.
Now, we need to find the value of log 0.225 base 10. We already know that 0.225 = 10^y, so we can rewrite the equation as:
10^y = 0.225
To solve for y, we need to take the logarithm (base 10) of both sides:
log (10^y) base 10 = log 0.225 base 10
Using the property logb(x^y) = y * logb(x), we get:
y * log 10 base 10 = log 0.225 base 10
Since log 10 base 10 equals 1, the equation becomes:
y = log 0.225 base 10
Now, we can substitute the given values into the equation:
log 0.225 base 10 = y
log 0.225 base 10 = log 0.225 base 10
Therefore, the value of log 0.225 base 10 is y = log 0.225 base 10 = log 0.225 base 10.