Find x,such that logx=4h minus k divided by 2 leaving your answer as a surd
logx=4h minus k divided by 2 , or
logx = (4h - k)/2 OR logx = 4h - k/2
Since you didn't specify the base, the default base is 10, so
first interpretation:
x = 10^( (4h-k)/2 )
2nd interpretation:
logx = 4h - k/2
x = 10^(4h - k/2)
either way, can't see where surds enter the picture.
well, it would be
10^( (4h-k)/2 ) = √(10^(4h-k)) = √10^4^k / √10^k = 100^k / √(10^k)
or something like that
To find x, we need to isolate it in the logarithmic equation.
We have the equation:
log(x) = (4h - k) / 2
To eliminate the logarithm, we need to rewrite it exponentially:
x = 10^((4h - k) / 2)
Therefore, the value of x is:
x = √(10^(4h - k))
This is the simplified form of the solution, expressed as a surd.
To find the value of x such that log(x) = (4h - k)/2, we need to solve for x.
Since the equation involves a logarithm, we can rewrite it as an exponential equation to eliminate the logarithm. Recall that the logarithm is the inverse function of exponentiation.
First, we need to understand the surd notation you mentioned. In mathematics, a surd is a square root or nth root that cannot be reduced to a whole number or fraction. Instead, it is represented in radical form (√x) to indicate the presence of a surd.
To solve for x, let's start by rewriting the equation:
log(x) = (4h - k)/2
By applying the exponential function to both sides, we can get rid of the logarithm:
x = 10^((4h - k)/2)
Now, if we want to leave the answer as a surd, we need to express the exponent (4h - k)/2 as the root of 10. We can rewrite it as:
x = 10^(((4h - k)/2) * 1/2)
Next, simplify the exponent by multiplying the two fractions:
x = 10^((4h - k)/4)
Finally, expressing the exponent (4h - k)/4 as √x:
x = (√10)^(4h - k)
Hence, the value of x that satisfies the given equation is (√10)^(4h - k), where (√10) represents the surd.