log8(768 x 16)
--> the 8 is a subscript to log
--> please show steps.
log8(768*16) = log8(12288),
8^x = 12288,
Using Base 10:
X*log(8) = log(12288),
Divide both sides by log(8):
X = log(12288) / log(8) = 4.528320834.
thanks
To solve the logarithmic expression log8(768 x 16), we will use the properties of logarithms.
Step 1: Apply the logarithm property log(base a)(b * c) = log(base a)(b) + log(base a)(c). In this case, we have log8(768 x 16) = log8(768) + log8(16).
Step 2: Simplify the logarithms by evaluating the expressions inside. We have log8(768) and log8(16).
To evaluate log8(768), we need to find the exponent to which the base (8) must be raised to obtain the argument (768). In other words, we need to find x in the equation 8^x = 768. To do this, we can write 768 as a power of 8: 8^x = 8^3. Therefore, x = 3.
Similarly, to evaluate log8(16), we need to find the exponent x in the equation 8^x = 16. Since 8^2 = 64 and 8^3 = 512, we can see that 16 is between 8^2 and 8^3. Therefore, x will be between 2 and 3. To find a more precise value, we can use interpolation or estimation. In this case, we can estimate x to be around 2.5.
Step 3: Substitute the values we found back into the original expression. log8(768 x 16) = log8(768) + log8(16) = 3 + 2.5 = 5.5.
Therefore, log8(768 x 16) equals 5.5.