What is the answer to log_{x-3}(x)= 9/5 ?

The answer to log_{x-3}(x)= 9/5 is x\approx 5.60554…

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log_{x-3}(x)= 9/5

lo g_{x - 3} (x) = \frac{9}{5}

x \approx 5.60554 \dots

Solution steps

lo g_{x - 3} (x) = \frac{9}{5}

Apply log rules

\frac{ln ( x )}{ln ( x - 3 )} = \frac{9}{5}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (x) \cdot 5 = ln (x - 3) \cdot 9

Apply log rules

x^{5} = (x - 3)^{9}

Solve

x^{5} = (x - 3)^{9} : x \approx 5.60554 \dots

x \approx 5.60554 \dots

Verify Solutions:

x \approx 5.60554 \dots

True

The solution is

x \approx 5.60554 \dots

n \cdot lo g_{10} (n) = n

lo g_{10} (x) = 6.33

lo g_{10} (3 x^{2} - 2 x) = 0

lo g_{9} (x^{2} - x + 3) = 0.5

- 1 + ln (x + 3) = 0

What is the answer to log_{x-3}(x)= 9/5 ?
The answer to log_{x-3}(x)= 9/5 is x\approx 5.60554…
Solve for x: log_{x-3}(x)= 9/5
The solution is x\approx 5.60554…