Solve =1.52-0.05916/5*log(1*10^-2)(1*10^-5)^8/(1*10^-8)

$$= 1.52 - \frac { 0.05916 } { 5 } \times \log \frac { ( 1 \times 10 ^ { - 2 } ) ( 1 \times 10 ^ { - 5 } ) ^ { 8 } } { ( 1 \times 10 ^ { - 8 } ) }$$

Evaluate

$$1.922288$$

Solution Steps

Expand \frac{0.05916}{5} by multiplying both numerator and the denominator by 100000.

$$1.52-\frac{5916}{500000}\log_{10}\left(\frac{1\times 10^{-2}\times \left(1\times 10^{-5}\right)^{8}}{1\times 10^{-8}}\right)$$

Reduce the fraction \frac{5916}{500000} to lowest terms by extracting and canceling out 4.

$$1.52-\frac{1479}{125000}\log_{10}\left(\frac{1\times 10^{-2}\times \left(1\times 10^{-5}\right)^{8}}{1\times 10^{-8}}\right)$$

Cancel out 1 in both numerator and denominator.

$$1.52-\frac{1479}{125000}\log_{10}\left(\frac{10^{-2}\times \left(10^{-5}\right)^{8}}{10^{-8}}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$1.52-\frac{1479}{125000}\log_{10}\left(10^{6}\times \left(10^{-5}\right)^{8}\right)$$

To raise a power to another power, multiply the exponents. Multiply -5 and 8 to get -40.

$$1.52-\frac{1479}{125000}\log_{10}\left(10^{6}\times 10^{-40}\right)$$

To multiply powers of the same base, add their exponents. Add 6 and -40 to get -34.

$$1.52-\frac{1479}{125000}\log_{10}\left(10^{-34}\right)$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$1.52-\frac{1479}{125000}\log_{10}\left(\frac{1}{10000000000000000000000000000000000}\right)$$

The base 10 logarithm of \frac{1}{10000000000000000000000000000000000} is -34.

$$1.52-\frac{1479}{125000}\left(-34\right)$$

Multiply \frac{1479}{125000} and -34 to get -\frac{25143}{62500}.

$$1.52-\left(-\frac{25143}{62500}\right)$$

The opposite of -\frac{25143}{62500} is \frac{25143}{62500}.

$$1.52+\frac{25143}{62500}$$

Add 1.52 and \frac{25143}{62500} to get \frac{120143}{62500}.

$$\frac{120143}{62500}$$

Factor

$$\frac{317 \cdot 379}{2 ^ {2} \cdot 5 ^ {6}} = 1\frac{57643}{62500} = 1.922288$$