If loga4 = 1.585 what is loga36
Well, let's see. If a^x = y, then we can rewrite it as loga(y) = x. So, loga36 would be the value of x when a^x = 36.
Now, we know that loga4 = 1.585, which means a^1.585 = 4.
To find loga36, we need to find the value of x when a^x = 36.
But don't worry, I'm not x-rated! So let's multiply both sides of a^1.585 = 4 by 9 to get a^9x = 36.
Now, we can see that x = 9(1.585), which is approximately 14.265.
So, loga36 is approximately 14.265.
To find loga36 using the given information, we can use the property of logarithms that states loga(M^N) = N*loga(M).
In this case, we want to find loga36, which is equivalent to loga(6^2). Since 36 can be expressed as 6^2, we can rewrite loga36 as loga(6^2).
Using the property mentioned earlier, we can rewrite loga(6^2) as 2*loga6.
Now, we have loga4 = 1.585 and we want to find 2*loga6. Therefore, we need to find the value of loga6.
Using the same property again, we can rewrite loga6 as loga(2*3). Now, applying the property, we get loga(2) + loga(3).
So, we need to find the values of loga(2) and loga(3). Unfortunately, without the base value of a, we cannot determine the exact numerical value of loga(2) and loga(3).
Hence, without the base value (a), we cannot find the exact value of loga36.
To calculate loga36, we need to use the properties of logarithms. One of the properties states that the logarithm of a product is equal to the sum of the logarithms of the factors. Another property states that the logarithm of a power is equal to the exponent multiplied by the logarithm of the base.
In this case, we can write 36 as a product of its factors, 4 and 9. So, we have:
36 = 4 * 9
Now, let's use the logarithmic property mentioned earlier:
loga(36) = loga(4 * 9) = loga(4) + loga(9)
We know that loga4 is given as 1.585. Now, we need to find loga9.
To find loga9, we can express 9 as a power of the base a. In this case, 9 can be written as 3 squared (9 = 3^2).
So, we have:
loga(9) = loga(3^2)
Using the property of logarithms mentioned earlier, we can rewrite it as:
loga(9) = 2 * loga(3)
Now, we need to find loga3. Unfortunately, we don't have this information provided in the question. Without the value of loga3, we cannot accurately calculate loga(36) using the information given.
assuming base a,
log36 = log(4*9) = log4 + log9
Now, since 9 = 4^1.585
log36 = 2*1.585 + 1.585 = 4.755
Interesting, isn't it, that
log_a(4) = log_4(9)
??