which three statements are true?
a) if x= -10^4 then log 10 = -4
b)if x= 2^8 then log 2x = 8
c) log2 2= 4
d) if x= 3 then log10 3=x
e) log 10 256-2log 10 a/log 10 b
f)log 10 (a-b)= log 10 a/log 10 b
g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e
h) the gradient of the graph of y= e^x at x= 2is 2e
can you explain why? I don't get this
which three statements are true?
a) if x= -10^4 then log 10 = -4
b)if x= 2^8 then log 2x = 8
c) log2 2= 4
d) if x= 3 then log10 3=x
e) log 10 256-2log 10 a/log 10 b
f)log 10 (a-b)= log 10 a/log 10 b
g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e
h) the gradient of the graph of y= e^x at x= 2is 2e
a, b
To determine which three statements are true, let's analyze each option:
a) if x= -10^4 then log 10 = -4:
To evaluate this statement, we need to understand the relationship between logarithms and exponents. The logarithm of a number to a specific base gives us the exponent to which the base must be raised to obtain that number. In this case, we're given x = -10^4 and log 10 = -4.
Now, 10 raised to the power of -4 should give us x = -10^4. However, -10^4 actually equals -10,000, which means that 10 raised to any power will not equal -10,000. Therefore, statement a is not true.
b) if x= 2^8 then log 2x = 8:
Here, we're given x = 2^8, which means x = 256. To evaluate log 2x = 8, we need to rearrange the equation: 2x = 2^8. If we substitute x with 256, we get 2 * 256 = 512 = 2^9. Therefore, log 2x would be log 2(2^9).
Using the property of logarithms, log a(b^c) = c * log a(b), we can rewrite this as 9 * log 2(2) = 9 * log 2.
Since log 2 equals 1, we have 9 * 1 = 9. Hence, statement b is true.
Therefore, the correct answers are statements b.