What is the answer to log_{2x-1}(256)=8 ?

The answer to log_{2x-1}(256)=8 is x= 3/2

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log_{2x-1}(256)=8

lo g_{2 x - 1} (256) = 8

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

lo g_{2 x - 1} (256) = 8

Apply log rules

\frac{1}{lo g _{256} ( 2 x - 1 )} = 8

Multiply both sides by

lo g_{256} (2 x - 1)

\frac{1}{lo g _{256} ( 2 x - 1 )} lo g_{256} (2 x - 1) = 8 lo g_{256} (2 x - 1)

Simplify

1 = 8 lo g_{256} (2 x - 1)

Switch sides

8 lo g_{256} (2 x - 1) = 1

Divide both sides by

8

lo g_{256} (2 x - 1) = \frac{1}{8}

Apply log rules

2 x - 1 = 2

Solve

2 x - 1 = 2 : x = \frac{3}{2}

x = \frac{3}{2}

Verify Solutions:

x = \frac{3}{2}

True

The solution is

x = \frac{3}{2}

lo g_{5} (x + 6) - lo g_{5} (x - 2) = 1

ln (1 - 5 x) = - 2

lo g_{8} (\frac{5 x - 29}{11}) = 0

lo g_{- 2 x - 3} (3 x^{2} + x - 19) = 2

lo g_{2} (x) + lo g_{2} (4 x) = 4

What is the answer to log_{2x-1}(256)=8 ?
The answer to log_{2x-1}(256)=8 is x= 3/2
Solve for x: log_{2x-1}(256)=8
The solution is x= 3/2