What is the answer to (x-1)log_{10}(2)+(x+2)log_{10}(5)=10 ?

The answer to (x-1)log_{10}(2)+(x+2)log_{10}(5)=10 is x=10+log_{10}(2)-2log_{10}(5)

Solve for x: (x-1)log_{10}(2)+(x+2)log_{10}(5)=10

The solution is x=10+log_{10}(2)-2log_{10}(5)

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(x - 1) lo g_{10} (2) + (x + 2) lo g_{10} (5) = 10

x = 10 + lo g_{10} (2) - 2 lo g_{10} (5)

Decimal Notation

x = 8.90308 \dots

Solution steps

(x - 1) lo g_{10} (2) + (x + 2) lo g_{10} (5) = 10

Expand

(x - 1) lo g_{10} (2) + (x + 2) lo g_{10} (5) : lo g_{10} (2) x - lo g_{10} (2) + lo g_{10} (5) x + 2 lo g_{10} (5)

lo g_{10} (2) x - lo g_{10} (2) + lo g_{10} (5) x + 2 lo g_{10} (5) = 10

Move

lo g_{10} (2)

to the right side

lo g_{10} (2) x + lo g_{10} (5) x + 2 lo g_{10} (5) = 10 + lo g_{10} (2)

Move

2 lo g_{10} (5)

to the right side

lo g_{10} (2) x + lo g_{10} (5) x = 10 + lo g_{10} (2) - 2 lo g_{10} (5)

Factor

lo g_{10} (2) x + lo g_{10} (5) x : (lo g_{10} (2) + lo g_{10} (5)) x

(lo g_{10} (2) + lo g_{10} (5)) x = 10 + lo g_{10} (2) - 2 lo g_{10} (5)

Simplify

x = 10 + lo g_{10} (2) - 2 lo g_{10} (5)

x, y - 3 = - \frac{2}{5} (x - 2)

- 13 x + 8 = - 8 x - 7

6 m - 5 m + 2 = 10 + 2 m - 4

x, 6 x + 4 y = 6

12 - x = 3 x

What is the answer to (x-1)log_{10}(2)+(x+2)log_{10}(5)=10 ?
The answer to (x-1)log_{10}(2)+(x+2)log_{10}(5)=10 is x=10+log_{10}(2)-2log_{10}(5)
Solve for x: (x-1)log_{10}(2)+(x+2)log_{10}(5)=10
The solution is x=10+log_{10}(2)-2log_{10}(5)