solve for x by writing the equation in exponential form:
log sub 4 x=-2
log sub 5 (2x + 1)=2
nevermind. thanksss
IF LOG 4^X = -2 ANSWER IS 4^-2 OR 1/16
IF LOG 5^(2X + 1)= 2 ANSWER IS (5^2- 1 )/ 2 OR 12
To solve the equations by writing them in exponential form, you need to understand the relationship between logarithms and exponentials.
In the first equation, you have: log base 4 of x = -2.
To write this equation in exponential form, remember that a logarithm is the exponent to which the base must be raised to get the argument. In this case, the base is 4, the exponent is -2, and the argument is x.
So, you can rewrite the equation as: 4^(-2) = x.
Simplifying that, you get: 1/4^2 = x.
Squaring 4, you get: 1/16 = x.
Therefore, the solution to the first equation is x = 1/16.
Now let's move on to the second equation: log base 5 of (2x + 1) = 2.
To write this equation in exponential form, once again, the base is 5, the exponent is 2, and the argument is (2x + 1).
The equation can be expressed as: 5^2 = 2x + 1.
Simplifying, you get: 25 = 2x + 1.
Now, subtracting 1 from both sides of the equation gives: 24 = 2x.
Finally, divide both sides by 2 to solve for x, resulting in: 12 = x.
Therefore, the solution to the second equation is x = 12.