Solve for: log_{10}(25)-(1)/(3) * log_{10}(8)+3log_{10}(2)

Expression: $\log_{ 10 }({ 25 })-\frac{ 1 }{ 3 } \times \log_{ 10 }({ 8 })+3\log_{ 10 }({ 2 })$

Use $x \times \log_{ a }({ b })=\log_{ a }({ {b}^{x} })$ to transform the expression

$\log_{ 10 }({ 25 })+\log_{ 10 }({ {8}^{-\frac{ 1 }{ 3 }} })+3\log_{ 10 }({ 2 })$

Use $x \times \log_{ a }({ b })=\log_{ a }({ {b}^{x} })$ to transform the expression

$\log_{ 10 }({ 25 })+\log_{ 10 }({ {8}^{-\frac{ 1 }{ 3 }} })+\log_{ 10 }({ {2}^{3} })$

Use the logarithmic product and quotient rules to simplify the expression

$\log_{ 10 }({ 25 \times {8}^{-\frac{ 1 }{ 3 }} \times {2}^{3} })$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$\log_{ 10 }({ 25 \times \frac{ 1 }{ {8}^{\frac{ 1 }{ 3 }} } \times {2}^{3} })$

Write the number in exponential form with the base of $2$

$\log_{ 10 }({ 25 \times \frac{ 1 }{ {\left( {2}^{3} \right)}^{\frac{ 1 }{ 3 }} } \times {2}^{3} })$

Simplify the expression by multiplying exponents

$\log_{ 10 }({ 25 \times \frac{ 1 }{ 2 } \times {2}^{3} })$

Cancel out the common factor $2$

$\log_{ 10 }({ 25 \times {2}^{2} })$

Evaluate the power

$\log_{ 10 }({ 25 \times 4 })$

Multiply the numbers

$\log_{ 10 }({ 100 })$

Write the number in exponential form with the base of $10$

$\log_{ 10 }({ {10}^{2} })$

Use $\log_{ a }({ {a}^{x} })=x$ to simplify the expression

$2$