What is the answer to log_{10}(x/5)+3=5.3 ?

The answer to log_{10}(x/5)+3=5.3 is x=10^{2.3}*5

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log_{10}(x/5)+3=5.3

lo g_{10} (\frac{x}{5}) + 3 = 5.3

x = 1 0^{2.3} \cdot 5

Decimal Notation

x = 997.63115 \dots

Solution steps

lo g_{10} (\frac{x}{5}) + 3 = 5.3

Move

3

to the right side

lo g_{10} (\frac{x}{5}) = 2.3

Apply log rules

\frac{x}{5} = 1 0^{2.3}

Multiply both sides by

5

\frac{x}{5} \cdot 5 = 1 0^{2.3} \cdot 5

Simplify

x = 1 0^{2.3} \cdot 5

Verify Solutions:

x = 1 0^{2.3} \cdot 5

True

The solution is

x = 1 0^{2.3} \cdot 5

ln (1 - x) = \frac{1}{3}

50 = 11.936 ln (x) + 13.954

2 lo g_{8} (x + 5) = 3

lo g_{5} (m) = - 4

ln (x^{2}) = ln (10 x) - 3

What is the answer to log_{10}(x/5)+3=5.3 ?
The answer to log_{10}(x/5)+3=5.3 is x=10^{2.3}*5
Solve for x: log_{10}(x/5)+3=5.3
The solution is x=10^{2.3}*5