Question

Решить уравнение log4(8x+1)=2

Answer 1

ОДЗ : 8x + 1 > 0

8x > - 1

x > - 0,125

$log_{4} (8x+1)=2\\\\8x+1=4^{2}\\\\8x+1=16\\\\8x=15\\\\x=1,875$

Answer 2

По определению логарифма 8x+1=4^2

8x=16-1

x=15/8

Answer 3

To solve the equation log₄(8x + 1) = 2, you need to isolate the variable x. Follow these steps to solve the equation:

Step 1: Convert the logarithmic equation to exponential form. In general, if logₐ(b) = c, then aᶜ = b.

In this case, the equation log₄(8x + 1) = 2 can be rewritten as:

4² = 8x + 1

Step 2: Simplify the right side of the equation:

16 = 8x + 1

Step 3: Isolate the variable x by moving the constant term to the other side:

8x = 16 - 1 8x = 15

Step 4: Solve for x by dividing both sides by 8:

x = 15 / 8

Now, simplify the fraction:

x = 1.875

So, the solution to the equation log₄(8x + 1) = 2 is x = 1.875.