Question

Please help!! 50 points!!

Use the exponential equation below to answer Part A, Part B, and Part C.
35^x = 8

Part A: Explain the steps to solve the equation.

Part B: Rewrite the exponential equation in logarithmic form using the definition of logarithms.

Part C: Use the equation from Part B to solve for x. Round to the nearest hundredth

Answer 1

a) below

b) log_35 (8) = x

c) x = 0.58487

Explanation:

a) 35^x=8

apply the exponent rule

xln(35) = ln(8) → x = ln(8)/ln(35) → x = 3ln(2)/ln(35)

x = 0.58487

c) log_35 (8) = x

x = log_35 (8)

base form (Rewrite 8 in power)

x = log_35 (2^3)

log rule: log_a(x^b) = b*log_a(x)

log_35 (2^3) = 3log_35(2)

x = 3log_35(2)

x = 0.58487