What is the answer to log_{4x}(2x+5)= 8/5 ?

The answer to log_{4x}(2x+5)= 8/5 is x\approx 0.81550…

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log_{4x}(2x+5)= 8/5

lo g_{4 x} (2 x + 5) = \frac{8}{5}

x \approx 0.81550 \dots

Solution steps

lo g_{4 x} (2 x + 5) = \frac{8}{5}

Apply log rules

\frac{ln ( 2 x + 5 )}{ln ( 4 x )} = \frac{8}{5}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

ln (2 x + 5) \cdot 5 = ln (4 x) \cdot 8

Apply log rules

(2 x + 5)^{5} = 65536 x^{8}

Solve

(2 x + 5)^{5} = 65536 x^{8} : x \approx - 0.57968 \dots, x \approx 0.81550 \dots

x \approx - 0.57968 \dots, x \approx 0.81550 \dots

Verify Solutions:

x \approx - 0.57968 \dots

False

, x \approx 0.81550 \dots

True

The solution is

x \approx 0.81550 \dots

- 9 lo g_{2} (8 - 9 x) - 5 = - 41

lo g_{5} (x^{2} - 24 x) = 2

lo g_{10} (x) = - 0.26916

lo g_{10} (\frac{1}{x}) = - 6.34

lo g_{x} (5) + lo g_{5} (x) = 2

What is the answer to log_{4x}(2x+5)= 8/5 ?
The answer to log_{4x}(2x+5)= 8/5 is x\approx 0.81550…
Solve for x: log_{4x}(2x+5)= 8/5
The solution is x\approx 0.81550…