f) log_(2)3^5= log_(3^4)7= h) log_(2^3)5^8=

<br />The questions involve logarithms and their properties. The given expressions can be simplified using the power rule of logarithms, which states that log_b(a^n) = n * log_b(a).<br /><br />1. For the expression log_23^5, it can be simplified as 5 * log_23.<br />2. For the expression log_34^7, it can be simplified as 7 * log_34.<br />3. For the expression log_23^58, it can be simplified as 8 * log_25.<br /><br />To find the numerical values, we would use the change of base formula, log_b(a) = log_c(a) / log_c(b), where c is any positive number (commonly 10 or e). However, since the question does not ask for numerical values, we will leave the answers in terms of logarithms.