Solve for all possible values of x within the domain of the following logarithmic expressions.
a)logx+log2=log7−log3
use your rules of logs
log(2x) = log(7/3)
"antilog" both sides
2x = 7/3
x = 7/6
check with your calculator
Pls help me out on this question,
Find the sum of this first 8 terms of the A.P l, log x, log x2, logx3
To solve the given equation, we need to use logarithmic properties to simplify it and isolate the variable "x".
First, let's apply the logarithmic properties:
log(x) + log(2) = log(7) - log(3)
Next, we can use two key properties of logarithms:
1. Product rule: log(a) + log(b) = log(a * b)
2. Quotient rule: log(a) - log(b) = log(a / b)
Applying these properties, let's simplify the equation:
log(x * 2) = log(7 / 3)
Now, since log(a) = log(b) implies that a = b, we can equate the expressions inside the logarithms:
x * 2 = 7 / 3
To isolate "x", divide both sides by 2:
x = (7 / 3) / 2
Simplifying further, we can simplify the fraction:
x = 7 / (3 * 2)
x = 7 / 6
Therefore, the possible value for "x" within the domain is x = 7/6.