if Loga4=1.585 solve Loga36
3 = 4^0.792
so loga3 = 0.792 * 1.585 = _____
log36 = log(4*3^2) = log4 + 2log3 = _____
or,
36 = 4^2.585
so log36 = 2.585 * log4 = ____
Why did the math book go to the comedy club?
Because it wanted to solve logarithmic equations and have a good laugh!
Now, to solve Loga36, we can use the logarithmic property:
loga (mn) = loga(m) + loga(n)
Since the question provides loga4 = 1.585, we can find loga2 using the same property:
loga2 = loga (4 / 2)
= loga4 - loga2
= 1.585 - loga2
Let's solve for loga2:
2 = a ^(1.585 - loga2)
Unfortunately, without the value of a, we cannot find the specific solution for loga36. Remember that the logarithmic equation requires the base, which is missing in this case.
To solve for Loga36, we can use the logarithmic property that states: loga(xy) = logax + logay.
Given that Loga4 = 1.585, let's express 36 as a product of powers of 4.
36 = 4^2 x 4^1 = 4^3
Now we can use the logarithmic property:
Loga36 = Loga(4^3) = Loga(4^2 x 4^1) = Loga(16 x 4) = Loga(64)
Next, we need to express 64 as a power of 4.
64 = 4^3
Therefore, Loga64 = Loga(4^3) = 3 x Loga(4) = 3 x 1.585
Now we can calculate the value of Loga64:
Loga64 = 3 x 1.585 = 4.755
To solve for Loga36, we need to use the properties of logarithms, specifically the power rule.
The power rule states that log base a of a number raised to a power is equal to the exponent of that power. In mathematical terms, it can be written as:
loga(x^y) = y * loga(x)
Given that Loga4 = 1.585, we can rewrite it using the power rule:
Loga4 = loga(2^2) = 2 * loga(2)
Now, let's solve for loga36 using the power rule and the given value:
loga36 = loga(6^2)
Since 36 is equal to 6^2, we can rewrite it as:
loga36 = loga(6^2) = 2 * loga(6)
Now, to find loga(6), we need to relate it to loga(4) since that is the only value we have.
We know that 6 is equal to 3 * 2, and since the properties of logarithms say that the log of a product is equal to the sum of the logs, we can use this to break down loga(6):
loga(6) = loga(3 * 2) = loga(3) + loga(2)
However, we only have Loga4, which is equal to 2 * loga(2). So, we can use this information to rewrite loga(2):
loga(2) = (1/2) * Loga4
Now we can substitute it back into the equation for loga(6):
loga(6) = loga(3) + loga(2)
= loga(3) + (1/2) * Loga4
Finally, we can substitute this expression for loga(6) into our original equation for loga36:
loga36 = 2 * loga(6)
= 2 * [loga(3) + (1/2) * Loga4]
Therefore, the solution for loga36 is 2 times the expression [loga(3) + (1/2) * Loga4].