What is the answer to 0.025=-log_{10}(1/T) ?

The answer to 0.025=-log_{10}(1/T) is T=10^{0.025}

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0.025=-log_{10}(1/T)

0.025 = - lo g_{10} (\frac{1}{T})

T = 1 0^{0.025}

Decimal

T = 1.05925 \dots

Solution steps

0.025 = - lo g_{10} (\frac{1}{T})

Move

lo g_{10} (\frac{1}{T})

to the left side

0.025 + lo g_{10} (\frac{1}{T}) = 0

Move

0.025

to the right side

lo g_{10} (\frac{1}{T}) = - 0.025

Apply log rules

\frac{1}{T} = 1 0^{- 0.025}

Multiply both sides by

T

\frac{1}{T} T = 1 0^{- 0.025} T

Simplify

1 0^{- 0.025} T : \frac{1}{1 0 ^{0.025}} T

1 = \frac{1}{1 0 ^{0.025}} T

Solve

1 = \frac{1}{1 0 ^{0.025}} T : T = 1 0^{0.025}

T = 1 0^{0.025}

Verify Solutions:

T = 1 0^{0.025}

True

The solution is

T = 1 0^{0.025}

2 = lo g_{t} (25)

0 = - lo g_{3} (x)

ln (x) = 90

lo g_{e} (x^{2} - 3 x - 27) = 0

lo g_{8} (2 x - 3) = 0

What is the answer to 0.025=-log_{10}(1/T) ?
The answer to 0.025=-log_{10}(1/T) is T=10^{0.025}
Solve for T: 0.025=-log_{10}(1/T)
The solution is T=10^{0.025}