Solve this equation for x
Log3^2x+5 =1
I will assume you meant:
log3 (2x + 5) = 1
then 2x+5 = 3^1
2x = -2
x = -1
If otherwise, let me know
To solve the equation Log3^(2x+5) = 1 for x, we need to isolate the variable x.
Step 1: Rewrite the equation in exponential form.
In logarithmic form, Log base a(b) = c means that a^c = b. Applying this to the given equation, we have 3^1 = 2x + 5.
Step 2: Simplify the equation.
Since 3^1 = 3, the equation becomes 3 = 2x + 5.
Step 3: Isolate the variable x.
To isolate x, subtract 5 from both sides of the equation:
3 - 5 = 2x + 5 - 5
-2 = 2x
Step 4: Solve for x.
Divide both sides of the equation by 2:
-2/2 = 2x/2
-1 = x
Therefore, the solution to the equation Log3^(2x+5) = 1 is x = -1.
To solve the equation log₃(2x+5) = 1 for x, we need to isolate the variable x on one side of the equation.
Step 1: Rewrite the equation in exponential form.
Using the definition of logarithms, we can rewrite log₃(2x+5) = 1 as 3¹ = 2x+5.
Step 2: Simplify.
Since 3 raised to the power of 1 is simply 3, the equation becomes 3 = 2x + 5.
Step 3: Isolate the term with x.
To isolate the term with x, we need to move the constant term 5 to the other side of the equation.
Subtracting 5 from both sides gives us -2 = 2x.
Step 4: Solve for x.
To solve for x, divide both sides of the equation by 2:
-2/2 = 2x/2.
This simplifies to -1 = x.
Therefore, the solution to the equation log₃(2x+5) = 1 is x = -1.